You have to pay for a WIFI package on a cruise. Most block streaming sites like HULU, and they also block SKYPE. You can only connect to certain social media sites like Facebook and Google +. The fastest package offered is $14 a day. Your best bet would be free WIFI sites in port. You would be better off talking to your phone provider and seeing if you can pay for a temporary package that has free roaming for the Caribbean.
Beat me to it, option two, is to look at what your service provider offers, when I go to Europe I pay an extra 50$ and have cell service and a limited amount of data, then just use WiFi everywhere else, cell service in Europe is a great scam because there are so many carriers and they will all whack you for roaming fees if they can
Vodaphone in Europe, BITD I had a pay by the minute type burner phone I would just buy minutes for while in Europe, then with Vodaphone upgrading their service it was easier and cheaper to just buy the roaming package for the time I was there
I was on a carnival cruise last year. Wifi was pretty trash and expensive. The first day or so we had cell service. But my phone allows me to make wifi calls and texts so I was able to keep in touch with my mom while she had my son. ATT has a international day pass I forget how much it is 5 or 10 bucks a day. You can just use your phone like regular with no roaming charges. We were in the Bahamas they have a list of countries the day pass works it. Worth a look.