So do wild animals also have diseases, too. Humans ARE a disease, you got a problem with that? Many people trap wild animals who roam into the cities, they will trap them and put them out where they belong.
How would you feel if someone bigger than your or whatever sets a trap for you and you die. That's how mouse, rats and other wild animals feel the pain.
Cats who hunt for mouse are not the same as the traps they set because traps have poision in it and cats don't have poision in it. It's MORE natural when animals trap them for food, not to dispose them. People trap them just to dispose them. If there are hundreds or thousands of mouse/rats, you would have animal control to deal with it. If you have a few mouse, just trap them live and put it out in the wild far away. It isn't a problem.