Cat has poop stuck to bum.

My cat was a rescue from a pet hoarder and was taken too young from her mother. She has never learned to be that clean. She tends to get urine and feces on her backside. She seems to have much more loose skin under her tail and around her hindquarters than most cats. I used to wipe her backside with a wet cloth and would clean up the streaks on the floor (she drags her hind after using the box) but now that she is older and uses food for her fur, urinary tract, etc I can no longer get the smell out of her fur. I have not been able to enjoy her as a lap cat for years, and she has to be confined to non carpeted rooms and away from soft furniture. My question is - would surgery to tighten her skin around her hind help keep her clean. I would really like to solve the problem as she is a sweet girl and would like to give her more attention (like petting her on my lap) but she only gets a few minutes a day. Also she is stressed all the time because she is dirty, and even hides when the feces is really bad on her hind.