I wanted to second this suggestion that you might try to spend some time with a bichon or a small poodle. It’s true that they’re not fool proof anti-allergy dogs, but it’s also true that they produce less dander and don’t shed. If you bathe him weekly and keep his hair clipped short, you might find it’s less hassle than you expected.
Plus, you get the poodle brains and the lovely poodle temperament. I’m a huge fan of the breed.