We gave our new five year old granddaughter a pirate cruise on her first trip to Disney World (13 years ago). Her mother was the only person in her life until she met my son so she was apprehensive as well. After the cruise, she said "I knew Disney would do it right". And they did. They are so concerned about safety that all kids will have their life jackets checked before they board, any single child (like my granddaughter was) will be paired up with another child of the same sex and age so it's a buddy system (OP, your kids will be paired together), all kids must sit down while the boat is moving, all kids must be with their buddy while doing any adventures, and when they get back to the dock, no child will leave the boat unless the same adult who dropped them off is waiting with the receipt and a photo ID. That's how it worked 13 years ago so safety is a huge priority for the cruises.
I do want to add that if you possibly can, be waiting at the dock before the boat comes back. And if you have a video camera, well, aim it at the boat. That's all I will say about it. Brought my now daughter-in-law to tears.