What holds mouse urine best?

You could put some news paper. I used news paper bedding for my rats, and it soaked up the urine well, but if you're looking for something better, I'd suggest a car shammy (or Shamwow). You can get a couple so when you need to wash one, you won't be without one. If you're going to go a while without changing out the shammy/newspaper, you can always put some plastic wrap underneath it so it doesn't get into the wood. Just make sure your mice aren't chewing up whatever material you do decide to put down. I know mine love to shred everything they get their paws on.