Back in ‘77 Gary Gilmore flat out said “shoot me” because he didn’t want to go through all the other crap.
That’s all they need to do.
‘The Executioner’s Song.’ Chilling portrayal by Tommy Lee Jones. TV Movie, 1982. Not that we should shed one tear for the POS, but Tommy Lee did a great job in that role.
As I recall it, he was asked if he'd rather hang. He worried that "folks might not hang me right". Similar answer for electrocution.
However, when the interviewer asked about shooting, he said that he knew from experience that that was hard to screw up.