I've had to relocate animals on a few occasions.
When I lived in Kentucky, we had a racoon that was eating our cat's food, off the front porch. The city animal control officer had live traps that they would loan out to catch animals. It didn't take long to catch the racoon. They are scary critters to deal with. Pretty viscous. I relocated it a few miles out of town next to corn fields. Never saw it again.
Where I live now, when we first got there, we had a real big problem with cats in our yard. A son of one neighbor would bring home stray cats to his mother, who loves cats. The cats would dig up flowers out of flower pots, so they could use the pot as a litter box. And the flower beds also turned into litter boxes. We had one feral cat that had a couple of liters behind the shrubs in our front yard. So it became time to control the situation.
I bought a live trap and started catching cats that frequented our back yard. I would relocate them to rural farming communities, where I figured there had to be a good supply if mice and such, to keep them fed. It worked. It is very rare that I have a problem with cat crap in my flower beds and vegetable gardens any longer.
Are we talking like a 20w50?