Mousers can be very valueable, but you must remember that mice/rats carry diseases and can cause your animal to be quite sick if ingested. I am glad you are going the route of safety.
There are several really good mouse traps and they have really improved over the years. a good NO touch one is...
http://www.orthohomedefense.com/smg/...temId=cat50086
There is also bait that you can put out, but be careful that its in a spot where your kitty wont get it. if you use food in a trap, mice like peanut butter better than cheese. The cheese dries out and doesnt throw scent a long way. The peanut butter smells yummy from far away.
If you trap one or two a week, you will be free in no time. bait allows them to carry the stuff back to the nest, and you will wipe out the colony before you know it.