Mice are sentient, does that mean we should only use no-kill traps and then release the mice somewhere far away? Many urban pests have population numbers that are 50-100X higher per square mile in the city than they could sustain in the countryside. So if we could even theoretically capture them and release them in the countryside, most would die due lack of sufficient food, which also seems unethical. And simply releasing a pest on the other side of the city so it isn't bothering your house clearly isn't solving the problem.
Killing animals, particularly pests, seems like an inherent part of urban living. Is this unethical? I don't think so.