I don't know about your area, but here in the NYC area, no cat rescues will adopt if you are looking for an outdoor "mouser"...now maybe that's because of our dense population, but be careful if you go to a rescue.
ALSO having worked at one of the biggest shelters in the country, Maine Coons have a reputation for being one of the worst litter box users, so many of them are in shelters in our area. I don't think that you'd even need a purebred anything, though.
I agree with all of those people who said a feral cat or barn cat who has lived on a farm should give you the best results. YES, YES, YES spay or neuter and make sure you, at the very least, give rabies shots.
I have a regular domestic shorthair who was a feral cat and he chases all of the critters. We feed him (which keeps him at our house) and he still brings us presents almost every day...mice, rats, moles, baby bluebirds....and I have threatened him every time he even LOOKS at a chicken, duck or goose.
Try advertising on Craig's List for a Mouser and see what you get.
Good luck!