Chosen Solution

Cat chewed through cable below volume control. Any way to fix this ?

You certainly should be able to solder it, but soldering this type of ultra-flexible wire is a bit fiddly. See https://wiki.restarters.net/Headphones for some hints. You will need some form of strain relief so that tension in the cable isn’t borne by the solder joints.

It might be much easier to just buy a new cable: https://www.hyperxgaming.com/us/headsets