I used a 1000 ft/s pellet rifle on rabbits with great succes. Of course I have a small backyard and they were never more than 40 feet away. I have had more squirells run after a hit in or near the heart than I did with the rabbits.
If you reload for the Nagant, maybe you can load a low power round that would make less noise for the pests or, if they make them, load it with snake shot in one of those plastic cups that replaces bullets. (all speculative since I have never heard of anyone trying this).
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