I would try using baby wipes. I use them all the time on my horse during shows. They clean then up really well, and they are gentle. Oster sells a similar product like a baby wipe, but they are way more expensive and work the same.
Baby wipes work but doing just the area that you are speaking of he will be fine to give a fast wash too. If your really worried about it use some warm water. But afterwards I would suggest putting some either vasaline or Desitine in the area to help prevent him from getting sores.
I would use warm water and dry completely. Like another said, you can use a blow dryer, not all horses like it though. My palomino loves the blow dryer. You could also use baby wipes, like another said. If he has sores from the diarrhea, don't curry it off, otherwise it will hurt and he may object. But if he is tolerant and doesn't have sores, you could brush it off like you do with dry mud. Good luck!