Cats are good at what they do.
We have three dogs. The spend a great deal of time going after the red squirrels who visit our bird feeder tree, but they nearly always fail. The squirrel sits up in the tree and teases them, and then makes off when the time is ripe.
Maybe they might get one squirrel a year. They’re very good guards, and they keep the raccoons and coyotes away from the chickens, but they aren’t very good at catching and eating. Seems like the only animals they can usually manage to grab are skunks—and that is not the best choice.
Sounds like you could have some fun with a good pellet gun.