Ohh, one of my preferred WWII PoDs. Let's delve in it once again.
First of all, to work this PoD requires a Hitler with a different personality, or a really influential advisor that can talk him into moderation at the right moments, or the November 1938 assassination attempt to work (the plausible successors would be Goring or a Wehrmacht junta). Alternatively, Hitler slightly delays the acceptance of Chamberlain's terms at Munich, and the generals overthrow him.
IOTL, ever-charming Adolf felt *cheated* by the outcome of munich, deeming himself deprived of the chance to ride in Prague as a victorious conqueror, and so he invaded Czechia at the first opportunity. He utterly overestimated the Wehrmacht's strength in 1938, and was oblivious that a fully-shaped military coup was ready to spring if he had given the order to invade. Likewise, as it concerned Poland, he initially made some half-hearted attempts to woo Poland as an anti-Communist statellite, offering territorial compensations in Ukraine for the Corridor. But when Poland turned them down, he totally switched to the idea of conquering that nation and turning it into the first Lebensraum playground.
So we need a different Hitler or a different German leadership after Munich. But it is quite feasible.
As it concerns the consequences of leaving post-Munich Czechia alone:
Cons: without the pilfered gold resources of Czechia, German economy risks a crisis by rearmament overspending. To avoid it, the pace of rearmament shall have to be temporary slowed down. Also, without Czech industries and armaments, German economy shall be somewhat less powerful, and its army slightly less strong for a while.
Pro: the Western powers continue to deem Germany a reliable and trustworthy power that keeps its word about Munich and go on with the appeasement. Nobody really takes Hitler's bit seriously about the Sudetenland being his "last claim in Europe", since every informed person in Europe knows that recovering the Corridor has been a most dearly-felt irredentist aspiration of the German people at large since Versailles. But the Corridor, like Austria and the Sudetes still rank as "reasonable" irredentist German claims, which the Western powers are content to satisfy in order to win Germany as an anticommunist major asset.
Once Germany reopens the Danzig-Corridor issue, it is practically sure that Britain and France do Munich II. Whatever the initial diplomatic feints, in the end Germany is going to claim the 1807 borders, i.e. Danzig, West Prussia, and Upper Silesia, possibly offering Poland to keep an extraterritorial access to Gdynia. The Western powers are going to accept.
It is a coin's toss what Poland is going to do. The wise course would be to back down, since without allies, against a stronger Germany, and a quite likely opportunist Soviet attack they are hopeless. And ITTL Germany is still genuinely open to have it as an anticommunist satellite and not a Lebensraum playground. But interwar authoritarian ultra-nationalist Polish leadership was anything but reasonable, and they might think they can at least exhaust Germany in a war of attrition. However, if a German-Polish war occurs after Warsaw defies Munich II, and if Germany puts any decent effort at concocting a decent casus belli (e.g. an irredentist German insurrection in Danzig, which Polish forces move in to suppress), the Western powers are going to leave stubborn Poland to its fate.
WIthout the military resources of annexed Czechia, and the previous need to slow down rearmanent somewhat, the war with Poland is going to be somewhat more painful for Germany, but a complete victory nonetheless. Perhaps they take 2-3 extra months to win. Now, the Western powers would certainly object if conquered Poland was subject to the brutal OTL treatment, but we are assuming a more moderate German leadership, so the peace deal is going to be a "reasonable" one that the Western powers would accept without any big trouble: the 1914 borders for Germany, and vassallization of Poland.
Stalin's reactions are an incognita. Poland is never ever going to ask or even accept Soviet help, but a M-R Pact is ASB with the Western-German detente. IMO the most likely outcome is that Stalin gambles sending the Red Army to invade eastern Poland just like OTL, rather than risking the Wehrmacht in the Kresy. Neither Germany nor Russia are really ready to fight each other in 1939, so after some skirmishes and hasty negotiation, a border much like OTL would be drawn.
While the other great powers are focused on Poland, Italy is going to make its move. Without the German annexation of Czechslovakia, it is much less likely that Mussolini would blatantly annex Albania, and may well keep it as a satellite. However, he is almost sure to attack Yugoslavia, fostering Croat separatism and using it as a casus belli, in an alliance with Hungary and Bulgaria.
Differently from what other posters have stated, it is almost ASB for the Western powers to intervene for Yugoslavia if they are still in the appeasement strategy towards the Axis. Britain never gave a rat's butt about the integrity of Serbia's little empire (they would have cared for Greece, but Mussoloni is going to prefer Yugoslavia as a target), and France stopped to care when it switched to appeasement and abandoned the strategy of building up the Little Entente as an anti-German tool. Moreover, in the appeasement strategy, Italy too is useful as part of the anticommunist front and the Western powers would very much prefer Mussolini's ambitions to be vented up in the "harmless" western Balkans than on their own territories and colonies.
Yugoslavia is partitioned: Italy annexes Dalmatia, Slovenia and Croatia are set up as Italian satellites, Hungary annexes Vojvodina, Bulgaria annexes Vardar Macedonia.
Alternatively, it is also possible that Mussolini and his Balkan allies manage to get most of the above (except Slovenia and Croatia) if he makes the Yugoslav crisis part of the deal at the Munich II conference. The Western powers are quite likely going to accept claims on Dalmatia, Vojvodina, and Vardar Macedonia. Yugoslavia may either accept, or be left alone to fight Italy and its allies, as Poland. Musso wouldn't get his Croat satellite directly, but humiliated Yugoslavia would become even more instable, and a Slovenian-Croatian successful secession supported by Italy is quite likely to succeed anyway.
Hungary, having been rewarded with the southern Slovakia at Munich and Vojvodina later, totally joins the Axis camp. Even if Poland backed down at Munich II, Germany is in the position to slowly pressure Czechoslovakia and Poland into satellite status, by economic and political pressure, which the Western powers won't bother about.
What happens later in Europe is totally dependent on who is in charge in Germany and what Stalin decides to do. If it's a smarter Hitler, he spends the next couple years building up his military and coalition for the anti-Soviet crusade, which Mussolini eagerly joins, as well as Hungary and Poland, perhaps even satellite Czechoslovakia. Romania is a wild card, it may be wooed into the Axis, stay neutral, or be defeated by Hungary (with Axis support) into a war for northern Transylvania, and beaten down into Axis vassal status.
A detente largely ensures between the European Axis and the Anglo-French. The Western powers happily stay neutral in the Axis-Soviet scuffle, and buy popcorn, seeing their appeasement strategy giving fruit. They give support to whichever side seems to be losing, trying to foster mutual exhaustion. And indeed a peace of exhaustion, with borders someplace between the 1939 lines and the Dniepr, is the most likely outcome. Stalin would be fully alert against an Axis attack, and the Red Army certainly can't defeat the Axis without an Allied second front and Land-Lease. Moreover, Japan is quite likely to join for the Axis, as a solo attack against the undivided Anglo-French-American might is quite foolhardy. Otherwise, Japan remains mired in the Chinese quandary. Finland stays neutral (unless Russia attacks it fearing its move on Leningrad, when the war starts) and the Baltic states become a battleground one way or another. Memel is a non-issue since Lithuania cedes it without a fuss like OTL.
If someone else is in charge of Germany but Hitler, they never attack Russia. Most likely Stalin remains cowed by the Western-Axis detente and WWII is averted. At the most Stalin may attack Japan, which ends with Russia holding Manchuria and Japan holding Korea and Sakhalin. Japan remains mired in China for a while. China never goes communist or at the very most it splits into Red North and Capitalist South. It (or the southern half) eventually grows into modern levels without the terrible trials of the communist experiment. Germany remains the economic powerhouse and the dominant power of Europe, while Italy and Japan reinforce their great power status as they continue their industrialization to OTL post-WWII levels and beyond. America remains a global economic powerhouse, but a great power among many. The EU doesn't happen without a full Franco-German reconciliation, which is only likely if Russia becomes a threat. However a mini-EU made up of the Axis nations and Spain is quite likely. France and Spain face a difficult path to decolonization, as America, Russia, and perhaps the Axis too supporting nationalist movements. Both fascism and communism remain respectable ideologies for long, and the former never becomes a pariah. Communism may still get eventully discredited as evidence leaks of Stalin's crimes.
However, it is still quite possible, if the least likely outcome, that Stalin decides to attack Europe when he's completed the build-up and modernization of the Red Army. The man was paranoid and prone to make bad mistakes about the ability and willingness of other powers to fight, so it is quite possible he thinks the European powers weaker than they are, or that he needs to do a pre-emptive attack against the aborning European anti-Communist front. If this happens, a WWII still occurs, with the OTL roles of Soviet Russia and of Germany-Italy reversed. Japan isn't going to stay neutral, but it is a coin's toss which side it joins. America is only likely to join if attacked by Japan. Anyway, the anti-Soviet coalition eventually reaps a complete victory (how easy depends on whether the Euros have Japan or America as an ally). The Soviet regime is overthrown, Communism becomes the pariah ideology of the 20th century, Russia is cut down to 1992 borders minus East Karelia (if Finland was belligerant), Rostov-Don-Kuban, and Outer Manchuria. It may or may not experience a Putin-like nationalist revanchist swing later. Europe ends up divided between democratic and fascist (but non-genocidal) blocs, where each build their own mini-EU even more tighly-bound than OTL. When fascism falls, a federal EU is born.
mad