The dust from many types of litter would be very likely to cause respiratory and eye problems. Paper based litters are good if you make sure it doesn't stay damp, as toxic mold can grow in it. Pine based litters are pine, which also causes health problems. Corn based litter is good, but on a warm summer day it will start to ferment: E-yew!
I'm not sure about the stuff based on wheat hulls. I use aspen after trying several different things. It works well enough, and I like the look of it.
If you can find a cat litter that is guaranteed to be dust free (no clay litter is dust free), it might be OK, but I doubt those claims. Shredded newspaper can be used if the ink is soy-based, but again, it may get moldy when damp, especially in warm weather.