Yep, went there on our honeymoon.
There are tons of charter boats for cheap. The deepwater is right there, so they don't have to run far. We had a trip that was going to cost me $200 lined up but wife got sick the day before on a snorkeling trip (too many tequila sunrises!) and got leary of going out. They caught 3 sailfish that day
This was 10 years ago, so please be careful of where you go. Everyone of the locals will try and hustle you. The best advice is to find a cab driver and tell him you want him to be your guy, and they will be able to help you get anywhere and anything (be careful with that
), and they will keep the hustlers at bay. If you are at a resort, there is plenty to do there and the hustlers aren't allowed on that stretch of beach. Spend at least an hour at the WalMarks down there too, its got a parking garage!
So to answer your question about permit, I have no idea!