I have a hard time imagining Sweden would join the allies, unless they were actually attacked by the Germans. If Sweden had entered the Russo-Finnish war, Germany would stand back. As far as I understand, the USSR-Nazi pact was not an alliance, just a non-aggression pact. Germany, after all did not participate as a Soviet ally in the Winter War itself and would probably like to see Finnish independence from the USSR assured. I suppose it's possible that unexpected British successes in Norway coupled with poorer German performance in the invasion might tempt the Swedes to enter the war to protect their fellow Nordics from the Germans and fight them there instead of Sweden itself. Skana would certainly fall to the Nazis, but the Germans might have trouble pushing farther north against solid British/French/Norwegian/Swedish opposition. Who knows, it is remotely possible that a permanent Scandinavian front with ample British (later lend-lease) supply thru Norway might really pose a problem for Germany - probably postponing both the invasion of France and Barbarossa. Imagine the RAF and USAAF 8th airforce based in Sweden and Norway rather than england, just a relatively short flight to Berlin.
It would also radically change Scandinavia after the war. Sweden would probably also become a militarized NATO member and Finland an unwilling member of the Warsaw Pact. IT could also become a major flash-point for cold war crises.
It would also radically change Scandinavia after the war. Sweden would probably also become a militarized NATO member and Finland an unwilling member of the Warsaw Pact. IT could also become a major flash-point for cold war crises.