I used to know some folks who raised tiny Chihuahuas and sold them to parents of kids with allergies and asthma.
There is a vast range of types with these little fellows, from one that looks sorta like a tiny collie to a deer legged one to the usual big eared fellow who loves tacos.
Maybe your son could get near one of these, it's worth a try. If you know someone with a Chihuahua and could introduce them it may work.