it sounds like you're a little oversensitive. Cats are quite clean typically. Human animals aren't always that clean either!
anyway, is your kitten long haired? Some people have them groomed to what some call a "potty patch" where they keep the rear-end trimmed so you're less likely to get "clingers."
I've been looking into this type of trimming myself lately as my kitten sometimes gets a little stuck to him. When I notice it, I grab a paper towel or a tissue slightly damp with warm water, and try to get out what I can. This usually does the trick.
a good bathmat or doormat outside the litterbox will hopefully help alleviate your feelings about her paws afterwards.
if just knowing that she pooped is what grosses you out, then that's not something that can be helped. It sounds like she grooms herself like any normal cat should. I hate to ruin things for you, but every animal including us are somewhere in between our last and next poop!