I'm asuming you don't wanna go wireless since you're asking for metal cables.. But besides wirless, I dont think headphones have a cat proof version. However, I think there may be some methods out there to stop him from nibbling on the cables. I always used simple tape. It makes the cord look ugly and im not sure if its very user friendly, since when I used this method I didn't play games online yet and only used a headphone when mixing music..
I am presuming a kitten, then try wrapping tinfoil around your cables until they are out of the habit of chewing cables?
If not, try lining them with a thin bare cable spiralled around your cable and connect it to a 9V battery, this will not hurt the cat, just make it very unpleasant to chew on the cables (put a 9V battery on your tongue to get an idea of what this feels like, to powerful use a old 9V battery ).
I was going to suggest the same, but ........ You need to charge a wireless headset- ergo does not solve the wireless issue. I also hoped that the OP had already considered that move