If mine had to poop, it would run off my lap, poop on the floor, then run back to me lol I know still not good, but better than my lap.
Unlike contrary belief, rats are EXTREMELY clean animals. I mean of course their poop isn't going to smell good, but they are constantly cleaning themselves, and even clean food before they eat it. I've even heard some rats that are litter box trained? Now that would be awesome.