Unfortunately, you don't exit through the secure area at MVY.... you walk out through a gate in the fence on one end of the terminal building and then would re-enter the building for baggage claim, or enter and go to the other end of the building for security. The "secure" area is about 6 chairs to put your life back together after security and then an outdoor patio whose only bathrooms are in a trailer. In the off season, it's basically just two park benches and some pad-locked coolers, some restrooms inside a trailer, and open area with no roof. In the summer they put up a tent over it and add more benches.

You'll likely have to exit and go back in. They only let people in to security by flight. I tried to standby on an earlier Cape Air flight and they wouldn't let me through unless the agent came back to give me a cleared boarding pass. TSA had the passenger total they were looking for. There is a PreCheck line though which they took on a priority basis.

It's not necessarily just a matter of if the agent cooperates... but airline has to have an approved security plan on file with TSA for handling connections (if everything is done completely by the book). I've connected there on Cape Air and they've made me exit and re-enter.