Your link mentions an attempt to replace it with the guillotine, not due to any less unpleasantness for either the onlookers or the star of the show, but to assist in organ harvesting. That has a ghoulish aspect all its own but it does, after all, allow the guilty to pay a debt to society that he/she wouldn't be able to do otherwise.
I am not inclined to believe that there is a means of execution that is foolproof and "humane", even nitrogen asphyxiation, which is probably as close as it can get. A bullet to the back of the head is probably close. That, however, is quite as messy as Old Sparky.