I'd say that if you end up to have a cat, feed him enough. I personally think it isn't right toward the cat to not to feed him enough so he'd hunt better. My view is that cats very probably hunt even them are fed anyways since they have that instict to hunt. And if not, then it's might better to find other ways to get these mice.
Hopefully you or your boss manage to solve the mouse problem. Stepping on a mouse would be kind of horrid experience. I remeber back in gone years, our late cat brought a half-eaten mouse in front of our summer cottage door once early in morning. Dad, after waking up, stepped barefoot right on that mouse. What a nice way to start morning I bet...
"On hyviä vuosia, kauniita muistoja, mutta kuitenkaan, en saata unohtaa,
Että koskaan en ole yksin, varjo seuraa onneain.
Vaikka myrsky hetkeksi tyyntyykin, varjo seuraa onneain.
Ja pian taas uusin hönkäyksin, varjo seuraa onneain.
Hei tuu mun luo, pieneksi hetkeksi. Puhutaan, varjoni, valkoiseksi enkeliksi." Pelle Miljoona - Varjo seuraa onneain