We were on the inaugural, and called in the morning at Grand Cayman (recall that's the early arrival port, I think we were off the ship a little before 8). We ordered the ham and cheese, and the turkey as well as a PBJ. We told them to skip the cole slaw, and they asked "are you taking this off the ship?" We said yes, so they brought us extra chips. They did say that they weren't sure if the port authority would let us bring the food ashore. I figured if they said no, I'd just throw it away (bad attitude, huh?). We had no problems though. No one asked. We had brought a little lunchbag type cooler, and packed ice in a zip lock. Bring plenty of zip locks!!
The PBJ was good, as were the other sandwiches. The turkey does come with mayo, so if you're worried about spoilage, ask them to leave it off. In my opinion, the sandwiches were big (but I'm a small eater). The turkey was on a sub roll, and was about the size of a Subway 6 inch, but with french type bread. The ham and PBJs were on regular bread. I know the PBJ was a triple decker, and I think the ham was too. I ate half the turkey, DH ate the other half. DD ate most of a ham, and DH ate half a PBJ and we were all full.
We took them on our Capt. Marvin's snorkling excursion, and just ate as we went from one place to another. One other family had brought the chicken strips, and I'd have to say they looked easier to manage, as long as you like them cold.