When I dove with Discovery Diving out of Beaufort in April, we got on a smaller boat and 2 out of 5 of us threw up. 5 ft seas, I think... Definitely take Dramamine to be safe and try not to eat a huge breakfast before going out. That shop did not require an AOW. We dove the Caribsea which had a TON of tiger sharks around it.
I suspect you meant Sand Tiger sharks, aka Sand sharks? Actual Tiger sharks are whole different beastie, I think. I was on the Caribsea last week and I'm pretty sure the big flock of sharks hanging around were all Sand Tigers.