NewFantasia cables are really good quality and affordable.
I have cats too. They love Apple charging cables. Somehow that rubber just entice them to lick and then bite on the cables. First day I got Sundara, I found a bite mark on the original Sundara cables.
I bought these NewFantasia cables on Amazon for my Sundara.
https://www.amazon.com/dp/B08D8WMZ35
It is only partially braided. The bottom section is braided. The top section that split into left and right earcups are still rubber. So not guaranteed, but helps a lot. And these are cheap enough, assume they will last months.
In addition, now I put my headphone and cables into a drawer when not in use.