It almost sounds like your cat is not licking it's bottom after using the litterbox. I guess that is a cat's alternative to TP. Sorry that I can't give you any advice on a solution. Did you ask your vet?
Sometimes when my cats were kittens one of them wouldnt have their bottom cleaned b/c some drips of potty were stuck there, I know, stinky! But if theres just nothing there, probably the cat is not big on cleaning it so try to use those wet wipes for cats, kind of like baby wipes and wipe his bum clean. Hope you find some solution ! =_