I've never heard of diff responses due to fat content. If he is intolerant to cows milk, goats milk might also still be a problem. Have you tried other non-dairy milks? Coconut milk (the drinkable kind, not the canned one) is the one we use here. If he is getting hives, have you talked to your doc about seeing an allergist? Another thought... what would happen if you gave him a spoon full of oil? Wonder if you would get a similar response....
Anyways, sorry can't be of more help.