I use shop towels. I breed corns as well and their poops are VERY wet and very stinky. With the blue shop towel, I literally never have to scrub anything, ever. The shop towels completely absorb any liquid, and usually all that's left is urates powder. What can't be picked up with the used shop towel, I just bang out into the garbage and spray it down and wipe.
Seriously since I've started using shop towels I've never had to take a bin into the shower and soak it.
Only thing is shop towel is a bit more expensive than paper towel, but I find you have to use less of it. Also if you cruise the local Hardware flyers, I find it goes on sale. Home Hardware was recently selling rolls of it for $1.60 each so I bought about 20 of them, lol.