Little Pete, Bambi and even Bambi's momma often let me pet them, especially when I'm calm. People told me it's a gift that animals will approach me when I'm calm. I've had multiple occasions of them letting me pet them even though they are totally wild and not in places where tourists feed them. Yet I'm like you, reptiles are out. Alligators won't be given warning shots but may get invitation for dinner.
My hats off to ya for those of you who live in alligata country, I can't imagine going outside at night or go to the lake for quick dip and come face to face with a alligator, not for me.