I wonder why you havent tried bait stations? Use the inexpensive blocks of poison, in a container that the cats cant get into, place it where you know the rodents travel, they will eat in the station and take it back to the colony, and in 2 weeks everybody is dead for about $10.00 in rodenticide. Most poisons these days no longer have a secondary capability to kill a dog or cat or chicken that eats the corpse, (and most dogs and cats wont eat something already dead, most chickens avoid them too.)
We have these bait stations in our coops, under our house, and I renew them each year when I hear that irritating scritching sound in the ceiling or walls, and it goes away, slick as can be. No smell, no traps, peace.
Worth a try, and worth every penny, compared to having them running on your counters and food surfaces.... eck.
You can buy bait stations already made, or do what I do, a locking tupperware container, cut a hole in the side, and make sure the bait cant be pulled out by a paw. I tape it to the far end, so they have to crawl in and chew on the block. Cheap, disposable, clean.