We lived in a converted farm house when my children were little, they had every pet known to man-kind from horses, goats, rabbits, chickens, ducks, geese, dogs, puppies, cats, hamsters, rats, gerbils, chinchillas, snake, lizards, tarantula spider, stick insects, birds and fish.
They played outside most of the time, lived in wellies, came home absolutely filthy and were the healthiest kids and now extremely healthy adults.
Yes! mcem remind him to wash his hands but I'm sure he will be fine.
Also, the care of pets should always be supervised by an adult, as I'm sure you are aware.