First Time Disney Cruiser -Internet Service

[Calantha]

Yep, the OP stated they have Verizon which offers (along with at&t) an international travel plan that costs $10 per 24 hours. These plans don't work while the ship is at sea.

https://www.verizon.com/plans/international/international-travel/travel-pass/

There apparently are some options: https://www.verizon.com/articles/verizon-unlimited-plans/4-ways-to-stay-connected-on-a-cruise-ship/

Seems to vary by cruise ship though.