2nding this. OP, if you hold a moral point against killing animals, you would be counterbalancing the mice with a cat. The Newark Humane Society almost always has cats that they rescue from the streets or from Animal Control, which is a kill shelter.

You would save the life of the cat and gain a companion - yes, it's a responsibility to care for a cat but it will kill and eat the mice since that's what cats do by nature. The smell of a cat will deter most mice in the future until you or your landlord can find and fix their ingress points.