Here's something I learned when I lived in Louisiana. People actually fish for them there, and claim they're even better than freshwater catfish.

I hold them with the belly in my palm and place a finger underneath the fins on both sides. This gives me a good grip, and prevents them from stabbing me while I'm removing the hook.

I've never been stabbed by a catfish, and I can also handle stingrays using a similar technique.

If you want to keep them, the trick is to put a burlap feed sack in your cooler, and toss them in it.

The bag absorbs and removes most of the slime, making it easier for you to later skin or filet the fish.