This might sound a bit insensitive but you can be sure it was done gently and with love...
When Ivy was being treated for continence issues (stone/UTI) her white bum was very dirty and because it was warm weather and she was going outside a lot I worried about her drawing flies. So I did a 'targeted rinse' under the tap. Put the kitchen mixer on at the right temp, hold piggie securely in upright position, go in bum-first and a quick rinse down below - massage briefly with supporting hand, another quick rinse, then support the bottom with a folded towel to soak up the excess. This avoided her belly getting wet. She was a bit startled the first time but was always rewarded with a veg treat and it takes literally a few seconds. I had tried dabbing her with a wet cotton wool pad to get the worst off but she was obviously sensitive in that area so this method was more comfortable for her. She wasn't completely stain-free but she was clean while her meds were working.
I actually used to do something similar with my babies - one had apocalyptic nappies and there were not enough cotton wool pads in the world..!