on a sligtly more on-topic note:hm. Take a cat, and risk an infection, or take no cats, and deal with rats...
Oh. that's an easy enough answer. leave the cats behind, and be extra sure to keep all the food in rock pots, or nethercap barrels.
In my fort, I butcher ALL cats, but managed to cage and train a breeding pair of peregrine falcons. Chained 2 females next to a nest-box (plus a male somewhere else), I got myself a perpetual source of flying vermin hunters.
My fort now has about 10~20 falcons flying around constantly, murdering every vermin they could get their claws on. Even better! Since they fly, they frequently path outside of the confine of my fortress and reveal ambushes.
So in short, lot of falcons...
1. No living vermin anywhere.
2. Free ambush patrols.
Down side, of course, is that I'm getting a LOT of dead vermins outside.