First, these little lizards are not geckos. They are anoles. There are brown anoles and green anoles.
The little lizards are very fast. It'll be more like a quest to try and catch one. The obvious thing to do is try to grab its tail. But surprise, surprise! You will be holding the tail, and the lizard will be long gone. Don't worry, the tail grows back. But the idea of a wiggling tail-only in your fingers has an eeew-factor. I would give DS advice that the lizards are just about impossible to catch, so he knows what to expect and moves on.
As others said, don't have him get off any path to get closer to wildlife. There are snakes, ticks, insects you never heard of, sometimes gators, etc. in the grass and scenery. Central Florida is not like other places back home, and there are distinct separations between civilization and the Florida wild that must be maintained by average tourists.