[Young stormlord]

I know why Jon didn't use sword.
Spoilers->
He hanged Slynt by legs with a hundred foot long rope because of Slynt's words in Asos (just before Jon goes to parley wit Mance)
“Still,” Slynt said, “I will not have it said that Janos Slynt hanged a man unjustly. I will not. I have decided to give you one last chance to prove you are as loyal as you claim, Lord Snow. One last chance to do your duty, yes!” He stood. “Mance Rayder wants to parley with us. He knows he has no chance now that Janos Slynt has come, so he wants to talk, this King-beyond-the-Wall. But the man is craven, and will not come to us. No doubt he knows I’d hang him. Hang him by his feet from the top of the Wall, on a rope two hundred feet long! But he will not come. He asks that we send an envoy to him.”