You can cut off the jack and solder a new one. You also don't need specific cord, buy a new cord and add the jack. For non replaceable cords you can open up the headphones unsolder the old cord and solder a new one. Or you can cut the cable somewhere high and patch another cable.
If you can't do these things your self there is probably some cheap electronic repair shop nearby. Most likely cheaper than shipping new brand cable or replacement parts.
On side note plastic in one of my shure 840 joints broke and I managed to fix it by modeling and 3d printing it. They're working fine now. The only official way to fix that was to buy original head assembly and ship it, but that's almost as expensive as getting a new pair.
Repair is possible, just sometimes you need to be a bit creative.
If you can't do these things your self there is probably some cheap electronic repair shop nearby. Most likely cheaper than shipping new brand cable or replacement parts.
On side note plastic in one of my shure 840 joints broke and I managed to fix it by modeling and 3d printing it. They're working fine now. The only official way to fix that was to buy original head assembly and ship it, but that's almost as expensive as getting a new pair.
Repair is possible, just sometimes you need to be a bit creative.