Finland is not Ukraine. It was also part of the Russian Empire but the relationship was not very deep. Russia might respond by putting nukes in Kaliningrad, depending on what the US is going to do. There aren´t millions of Russians in Finland as a result of the dissolution of the USSR.
If Finland wants to be an American bitch, it can go ahead and do that. It won´t make it a safer place. In the 70s, upon hearing that the United States would tactically nuke Germany in a war scenario, the former German Chancellor Schmidt responded to his shocked colleauge by saying "Do not worry, I will declare Germany neutral if it comes to that".