M.B.
K.,
Best guess here - if he's been receiving cow's-milk cheese for a while, it isn't going to be the difference in cheese that gives him the allergy. Most won't like swiss or strong cheeses. He may still have a sensitivity to milk anyway - my son did until 18 months and we still don't push it.
Milk/cheese from a cow is such a small section of the food available. If you are worried, trust your instincts. They're usually right.
Goat's milk/cheese is a great option that is closer to your milk than anything else. My son loves the cheese, but isn't fond of the milk yet.
Good luck!
M.