It is reused for Greyback in Predator 2. I don't think City Hunter ever has it during Predator 2.
Which might be a nice callback to that since I don't think we ever see them using swords. Spears yes, but no swords in any of these despite Greyback having it on his person. I think he even has it drawn for the entirety of his interaction with Harrigan but he never uses it. Hunting Grounds is pretty much the only place I can think of where the sword gets used (even said weapon being based on and named after said sword).