Besides the U.S., I think the countries capable of expeditionary military operations would include the UK, France, Russia, and China. Seeing the British in action in the Falklands showed that they're barely capable of expeditionary operations on their own but they did nevertheless manage it. France has deployed troops in fairly small number to Africa and does have naval vessels like the Mistral class that are helpful. Russia similarly has ships capable of moving a relatively small force around the world and did demonstrate that capability in Syria. (Although they're probably tied up right now with Ukraine.) China has also sent small numbers of troops to Africa, and at least in theory has the naval capability of moving a smallish force around the world. China has never demonstrated that capability in a large scale operationally however.

I do agree with you that even a remnant of the U.S. Navy could probably effectively screen any of the above countries from actively aiding a secessionist bloc.

In terms of motivation, I'm almost certain that the UK and France would side with Union forces. Russia would probably love to help secessionists but they're probably unable to right now. That leaves China. I think that they would probably want to help because they know that it'd mean the end of their biggest geopolitical foe. But I don't know if they're capable of it, at least not yet.