Is there a specific foam recommended for radiator pipes coming up through the floor?
No foam product will stop them, they will just chew through it. Some of them will eventually kill the mouse, but there's always another one, and another one, and another one to pick up the task and eventually finish it.
Aluminum or steel flashing is the only tried and true method. I've tried steel wool, it didn't stop them. They didn't chew THROUGH it, but they grabbed onto it and pulled it out.
Your best bet is to stop them before they get any where near your radiator pipes. Check the perimeter of your home at ground level and fill any holes you find to stop mice getting though the walls and into the structure or under the floor. Mortar works best in masonry and scrunched up chicken mesh (or any fine metal mesh) works in awkward spots. Follow up any areas where you find droppings or other signs of mice to determine how they are getting in. It is often a challenge, they don't need much space to get in. Keep an eye on foodstuffs and move anything they are eating or using as bedding. If they can find no food they may well decide to move on...
Almost anything you put in the holes around the pipe that the mice can't pull out or chew through will cause the piping to make noise from contact with the flooring and the material. As mentioned by others, steel wool and foams will not work.I would have an exterminator get rid of the rodent problem.
You can buy copper mesh that's designed to keep rodents out. Stuf-Fit brand is one example, but there are many to choose from. Stuff some mesh in the hole, then saturate it with expanding foam to hold it in place. Keep in mind that you still need to eliminate the mice or they'll eventually find (or make) another hole.
Spray foam works great - easy and fast. Spray it and then when it is still wet and fresh insert steel wool at any access that mice can get to. The foam will expand all around the steel wool and he will not be moving the steel wool, and you can also add a little cayenne pepper on top before it dries.