There are trail traps made for rats, but they are made to drown them. They are made so more than 1 can get in the trap. Now if you find a trail in the water and set it so they have a small amount of room to get air it won't kill them. You could also call game warden and see if you could get a newsant permit. Muskrats are a pain but what you are telling us does not sound like a rat, more like a beaver.
