I noticed a lot of people say, "It's the dander that causes allergies," but that is not the only cat allergen. My Mom, Dad, and I are all allergic to cats. My Dad's allergy is to the fur and my Mom's allergy is to something in the urine. I'm allergic to the dander, something in the urine, and clumping cat litter.
There are natural alternatives you could use that don't have the chemical that makes it clump, but that isn't is a fool proof way to avoid litter allergies. My mom thought she was only allergic to the clumping litter and tried to have a cat with the natural non-clump liter but still had attacks because the allergen was in the urine itself. The special litter exists because some people are fine around the cat and the cat urine/poop but are allergic to the clumping litter only. Also, some people don't want their cats pawing at chemicals everytime they pee.
I'm not trying to discourage you or anything. I just wanted to warn you that there is more to cat allergies than dander. You may want to make sure your Dad won't have more trouble with the litterbox than the cat itself. : /