If you don’t like cleaning litter boxes, you might want to get an automated litter box such as the Litter Robot Open Air III, which looks like a futuristic space pod from a science fiction movie.
The idea is that the cat strolls in, does its business, and when it walks out, a timer waits for the litter to clump. Then the dome swivels to dump the clumped litter in a bag for you to dispose of later. That way you never have to scoop a litter box again.
Of course, the Litter Robot Open Air III does cost $499, so if not touching litter is important to you, then you know the litter box for your cat.