Here is a load straight out of the Speer manual #14. 33 grain TNT HP over 12.4 grains of H110 or W296 in a Winchester case and a CCI 500 (small pistol) primer. That is a starting load go up to 12.8 grains, but do not exceed it and do not substitute another primer, especially a small rifle primer, the load will be way too hot. It should get you around 3100 fps or a little more out of a 22" barrel. The 33 grain TNT is a short hollow point so getting in your magazine should not be a problem and it should perform well. Keep your distance under 100 hundred yards so the velocity is up and the bullet should not exit. You could try a 35 grain Hornady V-Max as well and drop the powder charge but .1 of a grain. I have had very good luck with the MidSouth 34 grain varmint nightmare HP's in a 22K Hornet at about 3150 FPS. I have mostly punched paper, but have shot 2 woodchucks at about 35 yards. No exits on either one of them and they expired on the spot. I am using this bullet in my straight Hornet as well, but again only punching paper so I do not know if it will perform well on fur bearing animals.
Here are a few pictures of targets with different loads out of my 22K Hornet
The MS bullets perform well, but the 50 grain is way too tough for what you want
The CZ should do a great job, been thinking strongly of getting one in 222 Remington
Good Luck and Good Shooting
