Just speculating here:

Bak in “Ye Olde Times”, it was said that the king was ordained by God, who is infallible. The king must therefore be infallible. As such, the King only selects infallible subordinates. If someone is sentenced to death by one of the kings subordinates (or the king himself), they have been indirectly sentenced by God, through his infallible messengers on earth. Therefore, the hangman is only acting as the “Hand of God”, carrying out the judgment indirectly passed by God himself.

Problem solved :)