I think the original version of "Hurt" (found at the bottom of the post) would probably fit Cyberpunk better though, atleast when you consider how the song sounds. Cash's cover would fit better in a sort of Western type of a thing, atleast to me... which is why I think it works so well for the Logan movie. As mentioned part of it is due to how the song sounds... but it is also partly due to that the meaning of the song sort of changes depending on which version it is, where I think Trents version again fits Cyberpunk better then Cash's version does.
As for other songs...
The lyrics of some of Marilyn Manson song fits in my mind to something like Cyberpunk. Soundwise I feel that most Manson songs fits actually. But then I am biased, since I have always felt that goth-like (music which I for one reason or another feel/seem/think is to some degree or another "gothic"... but might not actually be it in the actual sence of the word... XD ), and/or "darker" kinds of metal like this, seems to fit with something like Cyberpunk.
And the 4th and final song. from a group called "And One", is compleatly due to the name (Panzermensch), and some of the lyrics (which I don't really know, since I do not speak German... but some words I can sort of understand due to either Swedish or English words which are simmilar... so I am only guessing at what it actually means... XD ). I know that Panzermensch means "Tank Man/Human"... which I think fits very well for those highly augmented tank like dudes in a Cyberpunk setting. XD
Nine Inch Nails - Hurt
Marilyn Manson - Killing Strangers
Marilyn Manson - The Nobodies
And One - Panzermensch
[video=youtube;qi5nTb-NRFU]https://www.youtube.com/watch?v=qi5nTb-NRFU[/video]