First, I agree you don't need to worry about bridges on the ICW. I made two ICW trips on Eclipse with a 53ft air clearance.
About 10 years ago I made my first ICW transits on a Savannah 26, a big sister to Wizard without any problems. I certainly would have been happy to sail the Savannah to the Bahamas. After all, crossing the Gulf stream is only 50 miles, half the English Channel width.
However sailing onto the Caribbean is much more challenging. The passages are longer and the seas rougher. So if you sail alone and have a backpacker attitude you could cruise down the ICW and to the Bahamas in a Wizard, but I wouldn't take one further.
The best choice would be the Gypsy or Saturn. Or maybe the Skua, particularly if it hs a small cuddy as we fitted to Tucanu.
As you know, two Gypsys have crosed the Pacfic and a Skua has crossed the Atlanitc
I hope this helps you choose the right boat