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FIT is key - not just Length of Pull for recoil but all of the other stock dimensions as well.
With your hand/arm issue, shooting even a 20, especially with slugs IS going to transmit substantial recoil. Best advice would be to ask your ortho doc what your wrist/arm can withstand.
A 38/357 rifle shooting mild 38s will kill a coyote, as will an AR, both of which will have less recoil than a shotgun. If you insist on a shotgun, a .410 with buckshot or slug would offer the least recoil
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