Cannot help with the permit, offhand, but if you are going to Mystic, I assume that you are going to the Seaport. You should not need a Disabled Permit, there have always been plenty of parking spaces when I have been there. With a few exceptions, it is a really visitor-friendly place. You might want to bear in mind:
- The big on-site cafeteria shuts mid afternoon if you want some lunch,
- They have a second-day policy - ask when you get your admission, and you can get back in for free the next day.
The best way to get around Boston is on the Metro - they call it the "T". Parking when I have been there was not easy anyplace you might want to get to (except on Sundays). And, if you get to Boston, think about a visit to Salem and/or The Old Saugus Ironworks.
This might help with a permit if you have not already tried them:
but normally they only go to residents of the State.