Over-the-counter or prescription med.s; you can't just run down to the pharmacy on a boat. I like to take 24 hour Sudafed, Ibuprofen, triple antibiotic ointment (for scrapes, etc...), swimmer's ear preventive drops, Bonine (even if you're not prone to motion sickness), a pill form equivalent to PeptoBismol, antacid tablets, Imodium, Flonase (I like to prevent congestion & ear squeezes), Claritin, etc... If you shave under your nose & such to improve mask seal, be sure you've got a shaving razor. Tooth paste & tooth brush. Deodorant! Ear plugs in case people snore.
If you bring a Save-A-Dive kit with o-rings, could come in handy. Extra fin strap if you don't have spring straps; extra mask strap. Maybe bring an extra mask. If you bring a scuba tool, put it in checked luggage for the flight; at an airport in Grand Cayman they wouldn't let me on the plane with a 'tool.'
A little notebook with water-resistant paper (e.g.: Rite in the Rain, Wetnotes) can be good for taking dive brief notes & after-dive-notes for logging later, without worrying about all the dripping water & puddles.
Lycra socks, to protect your feet inside your boots/booties from multiple dives over multiple days. Water softens your skin. I wasn't a believer till I found out in practice. Get these.
If you take pictures, see if you have the capability to back up your memory card to your smart phone, but use a large enough memory card you don't have to erase after the dives. That way you've got backup in case of camera case flood, or loss of phone.
Charger cable for your stuff. Last trip, I forgot the lightning connection for my iPhone & iPad. Buying one at the airport tore me a new one! A little portable surge protector might come in handy; not sure about Blackbeards (haven't done that one).
Other people can add more. Some bring clothes pins to help hand stuff up outside; don't know how common that is. My tips are for live-aboard generally; from what I'm told Blackbeards doesn't offer you much personal storage space, so be mindful of that.
Richard.