I don't know of a use for the word hangman other than the executioner. I think Knopfler is using the term metaphorically. He is saying that the captain or those who are to scrap the vessel are the hangman or hangmen. They are, effectively, putting the ship down, putting it to death.

Now that I see the second answer below mine I like it!! I was not aware of that.

Still, the song makes it sound as if the captain steps aside and lets the hangman do his job of running the ship aground to be scrapped. I don't see how a derrick is used anywhere. I think the hangman is the person charged with "executing" the vessel.

it is A spar fixed on board a ship used for hoisting cargo, boats etc..although the term does come from a hangman named Derrrick......an executioner