Are you sure you're allergic to his hair and dander? That's one of the nice things about Yorkie's and Poodles. I call them hypo-allergenic dogs. My daughter and wife have animal (and other) allergy problems which is part of the reason we got Yorkies and neither has had any problems.
If his skin is that dry or has that much "dander" I'd be looking for a problem that causing a skin condition. Shampoo maybe? Bad diet etc. I've never seen anything on either of ours skin.
Most any other dog and it would make sense, but it doesn't sound right for a purebred Yorkshire Terrier.
Maybe some of the resident experts will come along and school us.
