Perhaps next trip you could just keep them in full hazmat suits out in the cockpit they could doff before entering the salon. You're a good sport.
I believe rec shark fishing is covered under the HMS permit. There are size , number and species limits and prohibitions. I don't think any fluke permit is required for rec fishing in the EEZ (3+ nm out) but the state of the port you return to would govern the rec, regs. Obviously both a state & fed commecial boat permit , plus quite likely add'l special limited fishery permits, are needed to sell any open season fish but it sounds like you are just going for fun.
Unless you really get serious about selling HMS fish , I'd suggest sticking with the Angling Category /no sale of any covered fish, rather than the commercial only General Category. Then again, you are a licensed operator, so you might think about the Charter/Headboat permit to keep your options open. It gives you a choice of fishing under Angling no-sale regs or General Cat. commercial regs with closed days and quota closures. Angling keeps things simplest though and has fewest USCG approved commercial offshore safety equipment requirements. I'm strictly Angling cat. these days and haven't been tuna fishing this year-yet. With the price of fuel a bit less palpitation-inducing this year I point the bow way out towards warmer water once again.
Here's a good NJ list ;
http://www.scottsbt.com/fishids/regsrecs/regsNJ.htm . Just keep in mind I don't believe it is legal to take NJ size 18" fluke for instance over there and land them later in NY state if you guys have a 21" min. size.
Not sure about down there but we can only keep 1 recreational bluefin per boat per day this year in a size slot limit 27" to less than 47", plus 1 bft 47" to less than 73". (Angling and charter/headboat fishing under angling regs. For charter/headboat ctaegory you cannot fish both angling and general category rules in 1 trip. 1st fish kept determines which category & it's regs.. )