Portsmouth Sea Scout

The first stop would be to your local Council office, which I believe is Daniel Webster. If you base across the river in Maine it's Pine Tree I believe. As with any new unit, you would need a sponsor, a Committee with at least 3 adults and a Skipper and a Mate adult leaders. You need at least 5 kids 14 years old and have completed the 8th grade.
Your sponsor does need need to be anything Maritime related. Your local church, Elks, VFW or school, would work. Who sponsors your Pack? Perhaps they will take this on as well. Committee, where to find them? Parents of teenagers, people who are already in Scouting. Friends and co workers, people who belong to your sponsor?
Get a copy of the Sea Scout Manual, the local council service should have one (although as there are no Sea Scouts currently in NH, they may not) or order one through the catelog. They are $13.00. There is a lot of good info on how a Ship is run. See if you can set up a first night, perhaps at one of those Maritime places you talked about to draw in interested youth. Plan a couple of quick things, a whale watch cruise, a tour of the CG station, the museum, a bowling night, anything that might draw them in. Let them plan the next event and go from there.
Look to the U. S. Power Squadron as a source of help. They have an agreement nationally to help Sea Scouting. The CG Auxilary or the local Coast guard station may help. You might try meeting at the CG Station? Then start the program in the book.
There is lots more, but I don't want to overwhelm you. There is a very active and successful Ship in Newbury port. I could hook you up with them if you are interested. We have a New England Flotilla, made up of all the Ships in New England and we try and meet occasionally. I can keep you posted. We have or can find training for you and the other leaders.
It's a great program and a lot of fun. It's very different than any other program you will ever do. Because it is teenagers and coed, there are many challenges and even greater rewards. It's easier because they are young adults, it's harder because they are teens. (You don't worry about boy friends, girlfriends, hand holding and more in Cubs!)
Like anything in life, you get out of it what you put in. I assume you've been to Sea Scout.org, if not visit there.
What ever you decide, good luck. Please keep me posted and let me know how I can help if you do decide to look into it further.