A Himmler succession would be theoretically possible but very unlikely in 1939. The officer corps loathed him, the SS network was still relatively underdeveloped in 1939, and the man lacked a legal backing for a takeover.
Since September 1939, Hitler had publicly and legally designated Goering as successor (in a speech and with a decree), so the main plausible alternatives are a Goering succession, if he's able to stabilize his power quickly and efficiently, or a period of infighting among the Nazi top hierarchy (if he is not), followed by an Heer coup.
In both cases, Goring and the generals were moderates that feared and did not want a general war with the West nor Barbarossa. So we won't see a German attack on the USSR. A compromise peace with the West is certainly not a given, but quite possible, since the leader that betrayed Munich and blatantly attacked Poland is dead. Moreover, Chamberlain is still at the helm, and there has been no invasion of Scandinavia or Western Europe and very little real fighting on the Western front, so the bad blood between Germany and the West is limited.
Of course, after the betrayals of 1939, Britain and France shall want facts, not promises, to concede peace. Germany may surely keep Austria, the Sudetenland, Danzig, the Corridor, and Upper Silesia (and with any diplomatic skill, Posen as well), but has to restore the independence of Poland and Czechia. Although it may surely bargain to keep strong economic ties with both and have friendly governments in Warsaw and Prague. Goring was a moderate and not really interested into Lebenstraum, he advocated a neo-Wilhelmine policy. As it concerns the generals, they wanted to recover Austria, Sudetenland, and the 1914 territories in Poland, but were not really interested in annexing Czechia or Poland. So it seems a bargain that they would sign. The "phoney war" would wind down into peace and be thought of in history books as a bizarre tailend show to the German-Polish War.
After a period of diplomatic coldness, detente would eventually ensue between Germany and the West. Mussolini is likely to exploit the confusion to attack Yugoslavia in combination with Hungary and Bulgaria, as philo-Italian Croat separatism stages an uprising, something the West would not interfere in (since Britain was not really interested in spilling its blood to support Serbia's little empire), and would seize a clear victory. Conversely, Italy would not attack British protege Greece without a general war. An Hungarian-Bulgarian War against Romania to recover Transylvania and Dobruja is also likely. So WWII as we know it would disappear in the mists of history. What happens later depends on Stalin's reactions to the Western-Axis detente. If he is cowed, Europe remains divided between democratic, communist, and fascist powers, but peaceful. Japan dares not face the full power of UK/France/USA alone, and is eventually forced to withdraw from core China by the embargo and Chinese resistance, although it remains a great power in possession of Manchuria and Korea. There may be a Soviet attack on Japan, whose most likely outcome is a stalemate, where Russia conquers Manchuria and Japan conquers Sakhalin.
If he gets paranoid/overconfident, he gets into pre-emptive/opportunistic attack mode, begins to make aggressive moves on the Baltic states, Finland, and Romania, which shall quickly evolve the uneasy detente between the four capitalist great powers to a tentative alliance, and escalate Euro-Soviet tensions to a full-fledged anti-Soviet WWII. In such a case, Japan has roughly equal chances of joining the Euro anti-Soviet coalition and backstabbing Soviet Russia or making an alliance of convenience with Stalin and invading South East Asia, which brings America in the war against the SovJap Axis. In both cases, Stalin is eventually curbstomped.