How can I stop mice from living in my rabbit's hutch? He's got a large hutch with an attached run, he uses a..

cat litter tray to do his business so he's quite clean but inside his hutch I find mice droppings, his hutch is outside all year round. I have a mouse trap that catches the mice wihout killing them, I wouldn't want to put poison down for the reasons that 1, it could harm my rabbit and 2, I don't think it's humane, if I could line his hutch with mosquito netting they would chew through it and it's near on impossible to line his hutch anyway. If the mice cause no health threat to the rabbit then I'm not that bothered but I worry about the cleanliness of the mice and the risk of disease. Is there a humane solution, if so, I would welcome your comments, Many thanks.