The short answer is - it can be. But it's a lot safer than kayaking in Scotland. The common conception of people new to paddling New Orleans is that everything is out to get you. An alligator is going to roll you while a snake strangles you and a turtle nibbles on your toes. Thankfully, that is not the case.
While an alligator gone rogue is a possibility, their general attitude towards humans is they simply do not care about us. Alligators are not going to tip or flip our kayak. We are silly looking monkeys floating on the water, and us and our boats are too large to want to mess with. Crocodiles, on the other hand, they would view as a viable food source. But we don't have those. And what about snakes, they are dangerous, right? - Yes, some species in Louisiana are venemous. But snakes prefer to hide and do not pursue people. Snakes consider humans a threat (for good reason) and will detour significantly if they see us.
"The best thing to do is just leave them alone. Alligators want to be away from you just as much as you want to be away from them."Jack Hanna, Director Emeritus of the Columbus Zoo
The real danger is 2 opposites: Drowning and dehydration. In Scotland, I had a very close call after dropping in too slowly from a waterfall, I was dragged underwater and pinned by the current. What saved my life was the whole kayak backflipping and throwing me out and away from the current. That is why I say kayaking in New Orleans is much safer. There are no fast moving currents, there are no steep drop-ins. You may drop 10ft of elevation in an hour, not in a second.That said, drowning is drowning. You want to avoid at all costs your kayak flipping. So no standing up, and keep the loads balanced in the kayak. There are a lot of reeds underwater you can't see so I also recommend carrying a small pocket knife in the event you become tangled.
The other danger I mentioned is dehydration. With the sunrays bouncing off the water, heat-stroke is a serious consideration. That means reapplying sunscreen, wearing a hat/sunglasses and carrying a gallon of fluid. Mercifully, the oaks provide shaded pit-stops and you always have the option of going for a quick swim. Provided you don't mind the wildlife.