Its not an importation issue. Even if you transport the article to another country, it remains your personal property. Unless there is some kink, as long as the firearm was purchased in the United States, there is no issue. Anyone hunt in Canada? Did you export/import? Travel, overseas, often with firearms, hasnt been an issue. The Swiss are most civilized, try and avoid stopovers in England if possible.
There are allowances made for personal property transported beyond our borders, then returned. Had more trouble with cameras and electronics at customs, here and abroad. Ensure you can provide proof of origin (receipts) for anything that looks expensive. Otherwise things get kind of screwy if someone decides you should pay duty.
Could this be a problem, especially at present? Damn right. Seen too many third class functionaries make astounding leaps of logic based on incomplete or inaccurate understand of laws and/or regulations. Might not be the most prudent time to test this mate. Hate for someone to mistake you for a pirate.
Luck
Alac
Steve, is there a disclaimer posted? "Any information posted herein shall not be construed as legal advice..."etc? Just a thought, maybe I missed it.