Bearded dragons or leopard geckos could be OK. Beardies need quite a big cage and heater and lamp, but are friendly, sociable reptiles. They do eat alot though, and the live insects, reptile formula (for calcium) and veggies they eat need to be in constant supply from a dealer. Leopard geckoes are crepuscular, so don't need as much heat and light, but still need a lamp and vivarium with sand, moist area, hides etc. They shed their skin, so need extra care around that. They are usually sociable and can become very tame. Leopard geckoes eat a few crickets every day or so once adult.
You might be able to get special shampoos for dogs, a close cut poodle, for instance, but I'm not sure how effective they are. The hairless breeds might also be less allergic, but not sure if your step son would take to a hairless cat or dog.