I don't think butt baths are harmful. If you feel it is appropriate, I would just do one. Guessing a mild cleansing agent like Johnson & Johnson's baby shampoo might work.
 But much better to use a shampoo specifically formulated for pet hair that will not strip oils from the skin. A couple suggestions follow in the posts below.
- And got the T-shirt
The pH of the skin is different between human and animals, and can cause damage to the acid mantle of the pet's skin. You'll get a bunch of hits if you google "why use a pet shampoo instead of baby shampoo."
The vet said the next step was to stop the meloxicam and see whether Penny got noticeably worse. So far she seems pretty much the same, although she might be pooping standing up more often than usual. That seems odd given she'd just stopped the medication that was supposed to help her feel better, so it might be wishful thinking again. No new poop stains, though. The vet said after another week or two of observing her behavior without the medication we'll decide what to do next. He said the next diagnostic steps would be blood work and X-rays.
I vaguely recall one of my guinea pigs losing tiny clumps of hair. I guessed it might be a fungal infection, maybe a yeast infection (a yeast infection is a fungal infection). I gave her a Nizoral shampoo, which is supposed to treat fungal infections. I think there was some dandruff, too.
But there's a new problem: Today Penny weighed in 58.7 g lighter than a week ago (a 5% loss). She hadn't finished her pellet food yet when I weighed her, and usually she has because I usually weigh her later in the day, but there were only 5.7 g of pellets in the bowl (I weighed them). I have a vet appointment for her this evening.
Anyway, the vet did a physical exam and couldn't find anything wrong; he said that Penny looks great for six years old. (The physical exam didn't seem as thorough as the one she got at her well checkup last month, though. It went a lot faster.) He recommended X-rays and blood work. Penny had to be sedated for the blood work, but when they put the little anesthesia mask thing on her she started making a gurgling/wheezing sound, so they aborted the anesthesia because they were worried Penny would aspirate some of the leftover food guinea pigs always have in their mouths. So, no blood work. The X-ray showed a lot of excess gas in Penny's digestive system; I didn't get to see the X-ray because the computer system wouldn't let the vet pull it up, but he said there was a lot of excess gas. He said it looks like a weird case of GI stasis where Penny is somehow still eating and pooping normally even though her digestive system isn't working correctly.
The vet prescribed Cisapride (a GI motility medication) every 12 hours for ten days, and Penny got her first dose last night. I've been instructed to keep monitoring Penny's weight (but not too often) and behavior and to bring her back if things get worse, at which point they'll try to do blood work again. If Penny doesn't get worse, the vet recommends bringing her back in six to eight weeks for another checkup.
- And got the T-shirt
Why on earth do you suppose this vet doesn't think a guinea pig needs to weighed regularly? While I agree that there's no need to weigh more often than once a day, preferably in the morning, I can't figure out a reason why they shouldn't be weighed weekly.
The vet recommended blood work because GI stasis can sometimes be caused by other things that would show up in blood work, like bacterial infections. He also said that we don't draw blood from guinea pigs by clipping their toenails anymore because it's the equivalent of cutting off the tip of a person's finger. The vet I went to before I moved to where I currently live got blood samples that way, though, so I had thought that was standard practice. I don't know. The fact that he doesn't think weighing guinea pigs weekly is important makes me think I should take everything he says with a proverbial grain of salt.