We sailed the
Caribbean with a shotgun aboard for 15 years and never had any trouble. They never even sealed the gun locker even in countries that are supposed to collect and store your gun during your stay.
The important factor is that it is a shotgun, not a rifle and not a handgun.
Where you can have trouble:
Bonaire, I skipped it.
Mexico, I skipped it. For the rest simply report it when asked. If they start asking questions, say it’s secured in a gun locker and that was enough every time for us.
If I would go to
Mexico, I would vacuum pack the shotgun and hide it on a reef on the way in, then pick it up again on the way out.
In the
Bahamas we can take three guns incl. shotgun, rifle and handgun and a maximum of 250 rounds for each gun. Also, .308 maximum
power caliber.
Handguns are often problematic because they can be easily concealed, but not in the Bahamas. Also a tip: take the shotgun to your local CBP office, leave it in the car, go inside and ask for a form 4457. They will come out with you to check the
serial number and you get a form proving you took the gun abroad from the US so that you never get trouble bringing it back in.
Edit: and you hold the only copy of that form, there is no register.