I have photographed alligators from canoes, row boats, and more recently, kayaks
. While it is intimidating to be in a boat that is smaller than some of the animals, I have never seen one act aggressively toward me. I have had a few close encounters by drifting too close to an animal that I hadn't seen, but those ended by the animal simply leaving. Alligators are one of my favorite animals. They need to be respected, but aren't nearly as scary as they seem. Adult humans are simply too big to interest most alligators.
I haven't been in small boats in the Everglades. Most of the bigger waterways have very low concentrations of animals and I don't think you will find any different risks than I have seen in Okeefenokee, Peace River, or Myaka. I have spent a few weeks in the wilderness of the Everglades in houseboats, but our focus was fishing the gulf coast tide water, only passing through alligator territory on the way in and out. If you are planning to attempt the wilderness, I agree that you need to be well prepared for navigation (everything looks exactly the same out there) and backcountry travel. And the bugs (mosquitoes, no-see-ums) are a real test of self control, even if you are fully covered in netting and repellant.
I have never heard if freshwater fishermen have problems while reeling in fish. Splashing desperate fish attract predators (e.g., barracudas and sharks). In Alaska, we have to cut our lines if a bear approaches. I wouldn't be surprised if alligators can be a problem.
Take the canoe and have fun.