Riding on the Cape in the summer is not fun (or the islands, either, in my opinion). There are lots of drivers unfamiliar with the area and lots of elderly drivers who shouldn't be behind the wheel to begin with. That said, maybe you could ride the path that goes along the Canal on both sides. I think you can access that in Bourne or Falmouth. You could also do the Cape Cod Rail Trail, but that starts in Dennis, about 10 very crowded, trafficky miles from the ferry dock in Hyannis Harbor. If you can figure out a safe way to ride from Hyannis to Dennis, the Rail Trail goes all the way up to Orleans, with extension up to the National Seashore. It's pretty crowded, but I have been on it early in the morning, when it's not busy and it is quite nice then.
I had a really bad experience riding on Martha's Vineyard in the summer. Drivers expected us to stay on the bike paths (with driveway stops and intersections every block!) and we were constantly yelled and cursed at while on the roads. It seems like everyone is OK if you are on a cruiser, with no helmet, on a path, but as soon as you put on cycling gear and go out on the road, the whole thing changes. The hybrid would be great for riding there, so you can go on sandy paths, roads, etc.
Good luck!