the lightest weight single shot shotgun you can find loaded with 2's.
you're going to be going through thicker brush than you ever wanted to and chasing cat hounds is more about walking far and fast on snowshoes in thick cover and blowdowns than shooting.
single shot 20 ga or 16 is my go to gun for the last 45 years, or a 22 handgun but i dont allow rifles or handguns around my hounds, ricochet off branches and tree trunks are too dangerous to us, and not needed.
google Nelson Cole, Bobcat hounds. I have my bear hounds out of his musket dog, he and his son have videos out there I think called the Cat Men, gives you a view of what to expect.