I realize this is an old thread, but I thought I'd note that you can find some comments on the Sharps Navy purchase in another of McAulay's books, Civil War Carbines, Vol. II.
I provided the relevant quote and those from a few other sources over in another thread:
https://civilwartalk.com/threads/1859-sharps-navy-carbine.190786/post-2478686
You have one of generously 300 purchased. Nobody knows exactly how many were purchased by the Navy, so 300 is a swag, but there were just under 200 of these still in inventory by 1871. Stocks were then replaced if beaten up and the replacement stocks have an inspector's mark on them; most all barrels were relined with three groove rifling, although some six groove barrels were left if in good quality; the action converted for metallic .50-70.
Who knows how many still exist.. in addition to yours (assuming you don't have one of two others I'm aware of in the 43k range - 242 & 907) I'm aware of 13 others specifically.
I don't know where they were issued or how they were used. I've never seen any literature concerning these beyond the initial purchase and the conversions in '71. Given that the stocks evidently suffered some abuse and the barrels were shot out, it seems a safe assumption that they were deployed beyond simple guard duty on a dock. It's notable that the Navy purchased thousands of carbines overall before and during the War, so whatever they used those for they probably did the same with these, perhaps on a trial basis. The Navy was notably dissatisfied with the Jenks carbines, which were basically used (I gather) for smuggling interdiction (vis a vis the Revenue Marine Service) and such. That implies boarding parties to me, but I can only ignorantly speculate.