Magically, no taint, because they didn't use magic to carry out the executions, they used a sword. You can kill with a gun, a knife, a nuke, your bare hands, a garden weasel, whatever, and there's no First Law issue and no cosmic/magical taint from it.
Morally it's cloudier because the whole issue is morally cloudy.
Yeeeeahh.... Skeptically speaking, render someone immobile or helpless with magic so you can kill him/her with a sword, and you are safe from the taint because you didn't do it with magic? So kind of like tossing someone without immunity into a room filled with a deadly virus, if they catch it and die it really didn't have anything to do with you because the catching of the virus was all on the person that caught it..
