Does he have diarrhea? I was leaving my girl's hair long and she didn't have a problem with poop clinging to her hiney unless her poop was runny.
Other wise I would, as Robin suggested, clip his hiney and the hair around his little man and tummy.
At the last dog show I attended, I noticed the Yorkies,(well the females anyway) did not have long tummy hair. Basicly it looked like the hair was grown out from along the back, sides,legs, well and of course the head and neck too.
I would also just wash the dirty areas and reserve washing the whole dog just once a week. My vet says they carry a shampoo that can be used daily, but I don't think that is truely necessary. Unless he is laying and playing in his mess while you are out.
Oh, there are oils you can use too for his hair, I have read many a Yorky book that "mentions" them, just never specificly the name brand or what kind of oil. Like could I use olive oil, or does one use a grooming oil of some kind, but that might help his hair and of course wrapping it, might help too?