Which should I do?
1. Kill my cat, so I no longer have to feed it.
2. Give it away to somebody else, so I'm not the immoral one.
3. Feed it a diet that will cause it to die?
4. Other (please specify).
Keep the cat and after the current cat (or dog or any other meat-eating pet you might have) dies without your assistance, don't get a new meat-eating pet. In the meantime, replace at least some of your cat's diet with sour cream, cream cheese and other non-meat products that the cat might like.
This doesn't make you innocent of participating in animal slaughter, but at least you have a plan to stop participating in it.
Cats are lactose intolerant.
Besides, they eat meat by-products. No additional animals need to be killed to feed cats. Those were animals destined to die anyway. It's immoral not to use all of it.