In that the gun was most likely made for use in the UK, I go with Eurasian curlew. In the US, what are currently called whimbrels were once lumped into the curlew category--for instance, Hudsonian Curlews are now known as whimbrels. Here's a photo taken by a local birder of a migrating group of whimbrels or "curlews" on one of Georgia's barrier islands. Note the fiddler crab in one of their bills as they fatten up on the Georgia coast for migration to the tundra for nesting.
Curlews were once hunted on the Atlantic coast here in the U.S. Audubon's account and print of the Hudsonian Curlew:
https://www.audubon.org/birds-of-america/hudsonian-curlew He also did a print of the Longbilled Curlew with Charleston SC as a back drop.
All of the "curlews" bare a superficial resemblance to one another. In the hand, they are widgeon size.
Here are two of my curlew decoys carved by different makers from the Cape May, N.J. area probably in the 1890s. The smaller of the two has numerous shot holes on each side, more on the off camera side. Gil
