The allergy experts say that it is not the fur or dander that cause the allergies in susceptible people, but an antigen in the saliva. When I was looking into this for my husband's allergies, I was hoping that the hairless Sphinx cat might fit the bill, but their web site said that they did NOT have a reputation for being hypoallergenic. The two curly-coated Rex breeds (Cornish and Devon) have something of a reputation for being hypoallergenic, but I am not sure why. Possibly because their saliva does not stick as much to the curly fur. A number of allergic people I have known in my life-time (including my husband) have said that some cats bother them more (or less) than others. It seems to be extremely variable, not necessarily just long hair versus short hair. Most allergists say that if you can physically remove the allergens from the cat's fur and skin, by washing (even with plain water), then this helps quite a lot. They also recommend keeping the cat out of your bedroom. Another recommendation is to wipe down household surfaces frequently with a wet rag, rather than vacuuming, because the wet rag traps the dust which holds the antigens.
When my husband and I bought our current dog, we had her breeder send us some plastic wrap with her saliva on it. He had been allergic to the saliva (on his skin) of one of our previous dogs. You could perhaps do something similar to that if you find a cat you like. Even if you can't get the cat to lick a piece of plastic, you could run a clean comb through the cat's fur and then see if you are allergic to what gets caugth in the brush. If you are not highly allergic, then I'll bet your family can find one that works for you.
I hope this helps. Let me know if you have any questions.
Cat Veterinarian
Almost 30 yr as a practicing small animal vet.; experience in gen.medicine, surgery, emerg/crit.care