There are always get-together celebrations in Belize City for the 4th of July. They have hot dogs, beer, lots of fun and yes, they have fireworks. Fireworks are not illegal in Belize, you simply need to get a permit so that civil aviation, the fire department etc. is aware of the activity.
I haven't seen ads yet, but I think the 4th of July celebrations are held at Cucumber Bay just outside of Belize City.
Maybe once the US embassy moves to Belmopan, the 4th of July celebrations will move there too.
In the meantime nobody (ok, maybe a jerk or 2) will be offended if you want to wear your patriotic garb. Most locals find it amusing to see overly patriotic US citizens making sure we are aware that they love their country.