On my line - all the tech staff have 'dect phones' that are part of the ships system to communicate with. Our older ships have a pager system. Don't recall if the Sun even had pagers . . . you'll either be in your venues, the mess or your room - so you'll be easy to find ;-)
Most likely your cell might not work anyway when at sea, unless the ship has a satellite for this - and even then it's pretty expensive (around $3/minute). There are phone cards/sim cards/internet cards that can be used on the satellite system sold in the crew area to keep in touch with home.
AT&T seems to work better in most of the Caribbean ports, but if not a US territory or mainland, can be expensive.