How do you know it is the wire that is the source of your concern? Have you heard a set with different wiring? Have you heard other Stax electrostatics and compared the sound?
I have only heard the 009s once, at an audio show where it was powered by a Woo amp. I own a Stax Omega II Mk 1 headphone and a Blue Hawaii SE headphone amp. Because I heard the 009 in an unfamiliar system, I cannot really compare the two. I have read the comments of others who tend to agree that the 009 sounds brighter. Some actually like the additional top end lift of the 009. To me, the Omega II's are themselves a bit too bright, and they are extremely merciless when it comes to matching upstream components.
If you don't like what you are hearing, it might be worth trying a cable swap, but, there are a whole lot of other ways to alter the sound as well. The easiest, and usually most effective, is to swap tubes (assuming your amplifier/interface is tube based). I would next look into the interconnect cables to the amplifier. Even power cords matter too, so that is another place to investigate.
Good luck on your quest.