I like directness, so how about:

Please don't talk like that in front of me;
it makes me want to throw up.

Isn't that expression about catfish? Those fish really are hard to skin.

If the expression really bothers you, tell them why.

Agree. Just tell them that as a pet owner you don't appreciate those kind of comments. No reason to beat around the bush - just tell them straight up.

That phrase is about catfish, not felines.

People who use the expression usually have no idea of what it really means.

Trying to outwit an idiot usually backfires.

After all, you can't make a silk purse out of a sow's ear.

Handymac, as a lover of pigs (not to mention silkworms), I am horrified you'd use that expression! ;P

I think it's a little "indecent" to want to embarrass or publicly humiliate someone for using an expression, especially if they don't mean anything by it. If you wanted to politely tell them that you don't appreciate it, that would be one thing, but you've made it clear you want them to suffer and be humiliated.

I have 3 cats and I love them to death but I don't see the point in embarrassing people, especially in a professional relationship. They aren't directly threatening you or your cats and in all likelihood are just saying it out of habit.

It just seems pretty hypocritical for someone who spouts off about people being insensitive, offensive and indecent wants to retaliate in exactly the same manner.

I think this would be a losing situation for you if you respond. Most of us don't even think about a deeper meaning for expressions we've commonly heard and used and you'll come off as prickly and as a fanatic. Since the guy isn't actually "skinning cats" or even referring to actual cats, is it worth it? I would resent someone policing my speech when it had no malicious intent and didn't hurt anyone.