There is something in the FARs in regarding to operating outside the US airspace. From what I remember (20 yrs ago), you had to operate a certain percentage of the hours flown within the US airspace.
Nonsense. There are loads of N-reg operating in Europe, and they sure as hell don't cross the Atlantic on a regular basis.
The only thing you, as pilot, will need is the FCC radio license. Pure paper exercise. Reason: in the US the radio license is considered part of your pilot's license, doesn't work that way outside the US, you need a separate piece of paper. The only challenge (and that's a very real one!) is to navigate the totally insane FCC website.