I would worry more about the wind than the alligators!
I've seen kayakers out there around hog island and up toward Mason point and salt creek.
Just don't drag a stringer of fish beside your kayak and you will be okay.
I was fishing up near San Miguel creek several years ago out of my bass rig, and I had one of those metal clip chain stringers with about 8 nice white bass attached to it.
I was kind of working along with my trolling motor and the stringer over the side.
I felt a hard jolt and thought nothing of it as I thought I might have drifted up on stump and bumped the boat.
I caught another white bass and reached down and grabbed the stringer and lifted it up and all I had in my hand was a piece of chain about 10" long.
I didn't put two and two together right away and figured I snagged the stringer on that stump and ripped my stringer off breaking the chain.
Later on I spotted about a 14' gator a little ways down the bank, and that gator was as long as my boat and then it hit me as the light bulb went off.