Firm, consistent training. I've had shorthairs for almost 20 years. We've never had an issue with them chasing or catching animals. They are/were hunting dogs that don't put anything in their mouths unless they are told. Our big male loves everyone & everything and wants desperately to be friends with my barn cats. When we brought home the most recent barn cat, he was very anti-dog. Dell tried to make friends with him and got his nose smacked good. He won't even look at that cat even though he's been here long enough now that the cat wants to be friends but the big weenie dog won't let him get close enough to try. It's funny watching a 75 lb dog run away from a 7 month old kitten.
Honestly, I'd light his butt up with the shock collar and reinforce it with a very stern "NO CATS!" every time he was out of line.