The thing about Finland is that postwar, unless one contrives to have not just Soviet but Russian power collapse dramatically, is that Finland remains fundamentally not much less vulnerable than the hypothetical case of the other three Baltic republics somehow being independent postwar. Finland is a demonstrated tougher nut to crack, but I think everyone agrees that part of why Finland did not wind up a Soviet Republic before Barbarossa relates to really spectacular Soviet incompetence. When the Red Army advanced on Finland a second time, there was no way the Finns could hope to just fight them off again. And of course even with really staggering Red Army incompetence in the Winter War, Finland objectively lost that war too--compared to the grim scenario of total incorporation into the Soviet system they won, and Stalin lost, but in terms of territory lost and so forth, Finland lost. Just not as totally as one might have reasonably anticipated.
Postwar then, assuming either the USSR or some even moderately competent Russian regime exists, there are just three scenarios broadly:
1) Citing the plain fact that OTL (and probably here too though just maybe the author might see a way to prevent this) the Finns did, as a nation, join in with Hitler and were objectively speaking part of the Axis, and that it is not easy to stipulate Western Allied forces on the ground liberating Finland from Axis control, instead it is the Red Army defeating the Wehrmacht and other Reich agencies in effective occupation, the Soviets annex Finland, either on the same terms as the Baltic Republics--Soviet Republics under iron control of the Kremlin as allegedly integral parts of the USSR, or b) "fraternal people's republic" in the same manner as Poland, Hungary, eventually Czechoslovakia and East Germany, again under iron Kremlin control but on paper indirectly via domestic Communists (adopting various other party names as often as not, but it is easy to tell who is who).
2) via some probably unlikely gambit, Finland is effectively occupied by some non-Soviet force in the Allies, and manages to resist any Soviet bids to either rule outright or impose conditions on Finland. In the short run this might work, but the result is another major Cold War flashpoint, arguably much more volatile and sure to trigger some major Third World War avalanche than say US aligned Iran right there on the Caspian sea shore or NATO Turkey again right there. OTL this situation technically held in northern Europe too, as Soviet annexation of the Petsamo area of Finland put the USSR right onto the Norwegian border--but this was a very narrow border, far removed from major Soviet centers. An anticommunist Finland free to join some NATO type alliance--and let us face facts, Finland cannot assert an obnoxious belligerence to the Russians under any regime without strong allies--would be right up against Leningrad/St Petersburg and of course poised to choke off any Russian access through the Baltic. Thus, achieving this perhaps Utopian outcome involves coming much closer than OTL to damn near guaranteeing nuclear Ragnarok, unless one supposes (not too unreasonably actually) that the main thing preventing that OTL was that neither the Western powers nor the Soviets actually wanted WWIII and each side would in fact swallow bitter pills to prevent that--such as NATO's knife being right there at Leningrad's throat say. Despite the fact that OTL and probably here, the Finnish front of Hitler's advance was a grievous blow.
3) The OTL solution in fact worked out to a reasonable, IMHO anyway, compromise, that left Finland to its own truly free self-determination and in no way subject to Soviet rule--but at the price of strategic neutralization. Arguably Cold War Finland was less than free and certainly many Cold War attitudes in the West I was exposed to growing up assumed "Finlandization" was a disaster just short of outright Soviet conquest. But really, while the Finns had to be quite careful not to antagonize the Russians, this is actually inherent in their political geography, not some sinister Kremlin plot. They were not "free" to join NATO or rattle sabres in Soviet faces--but Finland was ruled of by and for Finns, in as liberal a regime as anyone has ever had.
Thus, if the author is sticking to the general plan of "limited butterflies away from Norway," a final postwar outcome pretty similar to OTL is no bad thing for the Finns.
I think it would be better for the Finns if they could somehow remain neutral throughout the war and have no complicity in cooperating with Hitler whatsoever--this of course presumes the Soviets give up their own schemes to gobble up the fourth Baltic republic too. Then neutralization of Finland postwar would be a matter of agreements at Yalta or wherever it is plainly in both Soviet and Western interests to keep, setting up Finland as a neutralized buffer state--if the Russians can be persuaded to not annex Petsamo, the buffer is complete. I've shared this wishful suggestion before that the deal somehow extend to the other three Baltic Republics too.
A big problem in trying to engineer a satisfactory long term solution is that the Western Allies included a lot of people, probably largely but not exclusively in the USA, who figured that the USSR would remain an allied partner in a peaceful and reasonably arbitrated postwar world order, that the UN (which was in fact the formal name of the Alliance late in the war) would work more effectively than the League of Nations had. Obviously most Westerners who hoped for this also had a rosy view of how Soviet society could function postwar. So--the negotiations for postwar settlement were not a matter of two blocs very frank and open about how they would be near-mortal rivals for generations to come, playing chess with each other to define two separate sustainable security spheres. Asserting that Finland should be part of a neutralized corridor of buffer states, with reasonable mutual assurances to guarantee neither side could grab the weakly defended states (again!) is a form of frankness about how it would be postwar that perhaps Churchill and Stalin might have dealt with each other with...but with the Western part of the Alliance being essentially under US control, neither FDR nor (if the author steps out of the limited butterflies ring and throws us a not too improbable curve ball) any other Democratic President likely to replace Roosevelt will be that blunt. The pretense will be there is no need for neutralized buffers because the whole Grand Alliance is one big happy family committed to postwar peace, this time for real. Naturally there won't be any NATO or Warsaw Pact, every nation big or small is equally safe under the UN Charter, war has been effectively outlawed! Naturally the Finns are perfectly safe, Naturally they won't be a staging area to strike at Russian vital cores (again!)
OTL Finlandization was not mainly a matter of some treaty or other, it was a reflection of geopolitical reality, and my major concern here is that the Finns are at any rate not worse off than OTL. We can do a lot worse than that!