I used to catch large snappers with my uncle. Never cruel - although you did need to kill them before you cooked them. My uncle's method was to hold a pliers in one hand and have the turtle snap at your outstretched hand - and then grab him by the lower jaw with the pliers. Then with the sharp knife in your other hand you would cut his head off, starting at the bottom of the neck. I think that is about as clean and quick as one could do it.
I know that I was probably more scared than those turtles. Me with the pliers having a 15 pound snapper chasing me backwards around his patio! “Come-on just GRAB his jaw. DON'T drop the pliers. Okay I got them, now here - just DO it!” (I'm glad that was back in the day before i-phones, it was sure comical looking back).
We would get some caught on our catfish lines. We used to get them to bite a large stick and then hatchet their necks. You had to be quick because they were almost always quicker. They taste better than you would think, although not good enough to make a habit out of them.
We still have all our fingers, though some of us came pretty close to getting one snapped off.