Let me qualify my statement about the water moccasins, I don't mean they will actually chase you as in follow you around if you run. They will on occasion come at you aggressively when they have plenty of other avenues of escape. The mouth open and tail wiggling is a defensive display. Their behavior is just atypical for most snakes, or other animals, who would move in a direction away from people. They are good swimmers, swimming on top of the water, and could easily move in another direction and against currents but will sometimes swim directly at you or towards boats out on the water (even when you're just paddling, not fishing which could be considered baiting them since they eat fish). They are commonly mistaken for banded water snakes, especially when you hear people talking about them dropping out of trees into their boats. I've never seen one more than a couple of inches above the water where they will sun themselves and hunt for frogs, fish, other snakes, etc.
We have plenty of alligators from about the middle of the state down to the coast, with far more the closer you get to the coast. Alligators don't make the news here often and the woman dying on Hilton Head was an anomaly; she was pulled into the water by the dog leash, not dragged in by the alligator attacking her. If the weather is warm enough for snakes and alligators to be out I'd be much more worried about mosquitoes, biting flies and ticks. Hopefully it'll have cooled off by then and none of them will be an issue.