There was some export of Brit guns to Japan. An Edwardian era shooting book backed up by Westley Richards claims that WR built a pair of their best droplocks for the Prince of Japan. It mentions unusual bird gold inlays on the guns made by design that came directly from the Prince, who apparently sent pictures of what he wanted on the gun. It would look like, while shooting birds doesn't seem a very Japanese thing to do, it was practiced at least by some of the nobility. And some market hunters, probably, all those pre-WW2 Japanese shotguns that surface now and then at American gun boards had to be used by someone. Last but not least, there were numerous diplomats, businesspeople, and qualified engineers, doctors, scientists, etc. whom Japanese invited to help Europeanize their industries and country - some of them could have brought hunting weapons along.