What area in Florida are you in? I am originally from the Fort Lauderdale area, and I seriously doubt that you are prohibited from using a gas powered hookah system on the beaches anywhere. The "no motorized" zones mostly pertain to boats where Manatees and people swim, and such is also implemented in the state parks. However, what you are doing is a simpler form of scuba diving and I grew up there on the beaches and watching the countless number of beach-based divers, and lot of them were using the hookah system.
If ever in doubt, call the department that is in charge of the beach you plan to swim/hunt at and ask them about the laws regarding gas powered air compressors for diving and get the confirmed (ok/denial) straight from the source and not from hearsay. The agencies you are looking for are Parks and Recreation, State Park HQ's and perhaps even asking the department in charge of Life Gaurd Duty may very well know if you can use this since they are the front line of enforcement of beach laws. I have not been in Florida in over 8 years since I have moved, but from the last time I was living there, I heard of no such laws, but things change over time.
More than likely if there are any laws, it would be ones that require you to refill the engine out of the water and off the sands of the beach and using specific containers to do such, which is not a bad compromise.
If you would like for me to help you to do some research and get you a real legal answer, let me know.
Oh and I would personally stay with the gas powered system if at all possible, if going with the electric hookah, be prepared to invest in a lot of power supplies and a reliable charging system.
I personally have a hookah-type compressor on my gold dredge called a T-80, I love it and you will too, there is no end to the possibilities and usefulness of the Hookah. These little compressors can even earn you darn good money if you are willing to use your air system to scrape barnacles off the bottom of other people's boats! I wish I would have had that idea back when I was in my 20's.
Have fun!