"Twangman" in the sense of twine dealer would fit to a twang knife and a twang cart (although I can't really tell if this was the typical equipment), but the whole setting rather suggests that the song's hero actually is a pimp. This would very well imply that he accepts sexual relations of his mot to other men on a strictly commercial base without problems, but shows malicious reactions, if they start to go beyond.

So, the expression "twang man"could be a kind of double entendre that allows to tell the story of a "cully" who falls in love with a whore and is bumped off by her pimp as a kind parody of typical broadside ballads about - if you like "innocent" - jalousy tragedies.

I wouldn't claim that this is the only possible interpretation of this song, but it seems to me that it is at least coherent.