Should people really be worrying about catsplosions? I mean, sure, having like 70 cats will hurt your fps but that's no big fucking deal. It's mostly no big deal because getting rid of already adopted cats, while more of a hassle than doing the same with unadopted ones, is perfectly doable.
Here's how to do it:
1. In a tight corridor, place a door, then an upright spike trap, then another door and a lever. The order has to be exactly as described, and you must build all of those things adjacently, i.e. with no spaces in between.
2. Link up the lever to the spike trap, and assign said lever to the dwarf whose pets you want to euthanize. Set the door that's nearest to the lever and mark it pet-forbidden. That way his pets will try to follow him but won't be able to reach him. Once they reach this door, however, it's probably best to mark the outer door as forbidden or pet-forbidden as well, as some pets (cats definitely, but other species might be different) are going to try and go back once they reach a pet-forbidden door. I understand that you might not want to do this, as it could be considered gamey; in this case, cat-killing might take somewhat longer, but that shouldn't be a problem.
3. Designate the lever for repeated pulling, until satisfied with the results.
Before you ask, yes, losing pets is distressing to dwarves, but that's nothing a good meal or admiring a nice piece of furniture won't cure.