As the seller, it is not legally your problem. It becomes the buyers problem when he has to register the boat.
Of course, a nice person (and it sounds like you are) would want to help the buyer to smooth out any problems related to this. To that end, you want to provide them with a bill of sale, which they can then use to get a Florida title issued. Only the vessel and trailer are subject to sales tax, so if the bill of sale itemizes separate costs for various items, it might save the buyer some money.
Having said that, if the boat is federally documented, then it is exempt from titling in Florida.
Official details here... http://www.flhsmv.gov/dmv/faqboat.html#6