According to the Mormon Church,

http://lds.org/new-era/1975/11/our-heritage-of-hymns?lang=eng

The tune used in "Poor Wayfaring Man of Grief" today IS the one sang at his martyrdom.

Incidentally, Willard Richards also survived the attack--didn't seem to be noted. He always attributed it to a miraculous prophecy Joseph Smith made to him in the summer of 1843: "Willard, the time will come when bullets will fly around you like hail, and you will see friends fall to the right and to the left of you--but there will not be so much as a hole in your garment." He got through with nothing but a grazed ear, and he was a man who weighed nearly 300 pounds.