There are no WDW alligator wranglers. Alligators are a protected animal and can only be removed by licensed professionals if they fit the nuisance criteria. There are alligators everywhere in Florida, including Disney which is in a swamp area. They rarely approach people who are not in/very near the body of water in which they live. I’ve kayaked past alligators about ten feet away many times, no big deal. Once one swam a few feet from me. Just stay out of the water, away from the bank, and don’t throw food into the water/onto the shore.