There's a picture of me as a kid holding a baby alligator. You can just tape their mouth shut, the jaw muscles to open their mouths are weak, it's closing their mouth that can crunch bone. I'm not sure the gators like it much though, lol.

On a tangentially related note, check out Gatorland if you're ever in Orlando. It's a fun time and one of the few remaining old Florida tourist attractions and a perennial field trip destination for the local school kids, that's why I've been there several times.