Congratulations on your upcoming wedding!
It will be difficult to find a cruise during the first week in July that has no teens or kids. However, based on most of your other criteria (on-board wedding on 7/4, dancing, shows, age mix, a fun ship, and kids programs that keep them occupied), I would suggest Princess.
Caribbean Princess has a 7/1/07 cruise to St. Thomas, St. Maarten, and Princess' private island in the Bahamas. The only thing is that this ship leaves from Fort Lauderdale, not Port Canaveral.
We did a vow renewal on Princess a couple of years ago and it was marvelous. I've heard they do a great job with weddings, too, and based on our experience with just a vow renewal, I believe it.
You might also want to look into Celebrity, as I was having trouble with their Web site this evening.