Which I think is Zhaleskra's poiny: if this is a proper gallows and the hangmen is competent, does the adventurer's neck break on the drop or does the adventurer 'hang around' awhile while the others have a chance to save him?
Well, then, you've answered the question - the issue isn't the hanging character, but the hangman. Have the Hangman make a Rope Use (or whatever his applicable skill) check. If he makes it, it is the equivalent of a coup de grace, if not, use the suffocating rules.
Unless the hangman's a vicious dude, and he willfully makes it so the character suffocates instead.