This is the most common way I see a snapping turtle get handled. Looks like your fingers or limbs would be safe this way:
This seems safe too but will depend on the size of the turtle:
First picture is an alligator snapper and the second picture is a common snapper - both being held safely as suggested. I double dog dare someone to hold an angry serpentina with the same method that fella is using on the macrochelys.