I had heard that once both Disney ships met in the ocean for fireworks on the 4th, however, no they dont do that anymore.
We sailed on last years July 4th Wonder cruise. At dinner that night, along with the regular menu, they offered a special "American" meal. I think it was something like fried chicken & ribs, but I cant be sure. Somehow, eating stuff like that in Tritons, when dress up, just didnt seem right.

They also had the waiters walk around waving flags to "Your A Grand Old Flag". Then they gave us special souvenier glasses(plastic) with champagne and they made a special toast.
The lobby had some red, white & blue decorations and balloons. Due to lightning, the sailaway party was held in the lobby and that is when they did the balloon drop, right as we sailed away. Some balloons had paper with a prize written on it inside so all the kids were popping them. It almost sounded like fireworks.
Oh and most importantly, the drink of the day was "Stars & Stripes"...strawberry daiquari, pina coloda, and blue curaco. Very yummy!