Infiltrate the mouse society. Breed with their women. Become one on of them. Undermine their authority from within. Install a puppet mouse state that works for you. Catch the mice.
Profit
It reminds me of that joke I used to find hilarious (I was 8, my humor has changed): Why do you wrap a hamster in tape? So that it doesn't burst when you fuck it. Just bringing it up because I'm curious to know how you plan on breeding with mice. (If you don't see how size would be a problem, I have bad news for you).
Profit