Finland would be in deep shit if they went and severed their ties with Germany, who at the time had 200 000 - 300 000 soldiers in Finland or in the vicinity, and on whom Finland was dependent on food, fuels and fertilizer. The wartime Finnish leaders knew this, and that is why they waited IOTL until Germany was weak enough not to be in a position to punish Finland very severely when they finally jumped ship in 1944.
Also remember that the Red Army helping the Finns to expel the Germans from Finland would mean the Red Army operating on Finnish territory. Once the Soviets are in Finland, it would might not be easy to get rid of them again - like the Baltic states found out IOTL.
In the end, ITTL Finland would come out of the war in a worse shape than IOTL. It might well be even more under Moscow's thumb than IOTL, a puppet people's republic and a member of TTL's *Warsaw Pact as well.