Take-out on the lower Cape?
I've only stayed on the lower Cape (Eastham and Truro) during the slow season (June and September) and the only places I used for take-out were for seafood. I can't remember the names of the places in Eastham and Orleans, but they were also fish markets and may still be open.
Although I haven't been there in a few years, the one place I always try to go to is Clem & Ursey's (http://www.clemandursies.com/) in Provincetown. They called it a "food ghetto" and it was a good description. I imagined that I was in Jamaica when I was there. I normally got take-out from there and took it to the beach, since it's not far from either Herring Cove or Race Point. Might be a little chilly off-season, of course...