For a beaver in a trap, a rimfire cartridge is fine. For a 50 yard shot on a swimming beaver, given the choices of cartridges you mentioned, I suggest a centerfire rifle cartridge loaded with Trail Boss. Load the .223 with Trail Boss powder. With Trail Boss, a 55 grain bullet can be shot out of a .223 with subsonic velocities (around 1075 fps with a 24" barrel). That's going to hit harder and penetrate better than a 22 LR without being explosive on impact. You might even be able to use a hollowpoint at those velocities and have it stay intact without much expansion owing to the design having integrity at triple that speed.
Besides Trail Boss, you can also use some other high speed powders in .223 like Titegroup and Clays. They achieve a similar velocity. Hodgdon publishes data for all three.
Besides Trail Boss, you can also use some other high speed powders in .223 like Titegroup and Clays. They achieve a similar velocity. Hodgdon publishes data for all three.
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