I've completed a two week long trip in the everglades two years ago. Alligator were quite often on my mind; I imagine they could snap the paddle if they decided to.
However boating in these water is a very popular activity and the maps are very well documented; hence I Imagine this never happen.
The most scary party is when you non intentionally corner an alligator in a bay or a stream. They move very fast agitating the water, very scary when you don`t expect it. They are just trying to run away. This happened maybe 3 or 4 times.
I did see a lot of alligators of different sizes. Maybe 10 or 15.
I think your concerns, just like mine was, is probably over exaggerated. Caiman are much smaller as well. I would be much more scared of other human beings if I was you
My two cents