1) Reb Shaye’le Karesztierer’s descendants have said that the segula is a baabemaaseh but if you want the picture it is online somewhere.
2) A cat is not recommended for indoor mouse control except in a warehouse. You are just exchanging one vilde chaya for another. Cats do more damage than mice. They are not domesticated and not affectionate – they just rub against you to mark you as part of their territory. Odor, hair cleanup, tzoiah cleanup, damage to furniture, carpets, stored food – all not worth it.
Poison traps do not leak any poison into the air. We all have worse poisons in our homes anyway.
3) Very few of the commonly sold products work. Best to call the pros.