As appropriate as that might be, nacl ... who ya gonna get to saw through his neck? Don't know if ya would find any takers for THAT ... and if ya did, I'd be wonderin' 'bout that particular volunteer, don'tcha know.
At least with a firing squad, you could put some blanks in the mix and give the shooters plausible deniability (to themselves) if any of them were even a little squeamish about the task.

The essential American soul is hard, isolate, stoic, and a killer. It has never yet melted. ~ D.H. Lawrence