In Finland planning heading up to Kuopio in the lakes and also going to Tallinn - it would be possible to take the train back to Helsinki and then the ferry across to Estonia but it would be a long day.
Flight is only one hour Kuopio to HEL and half an hour on to Tallinn - but according to the Finnair website there is only half an hour between one arriving and one leaving.
Even if there are no border formalities, there will be checked in baggage - can they be serious ? If not are you left to wander around for hours in the lounge ?