wow, my cat used to do the same thing ....
She leaves alone all the wires in the house except for the mic/headset cable ......
after 2 different mic's and splicing wires multiple times I gave up and switched to USB ...
I stuck a USB hub on my desk and run a USB cable along the back of my desk .... the cable never moves or attracts her attention ... so it has stayed "safe" from her thus far.
My headset connects to the USB hub, and I just leave the extra length of cable on the desk .. no cables hanging down tempting the kitty ... no chewed cables .... so far so good .....
If I catch her eyeing or messing with the cable ... then the next step is 1.) some type of cable management (I'm thinking PVC pipe behind the PC and desk ... where I can run monitor, printer, USB, second monitor, printer and monitor power cables, keyboard, mouse, etc from on the desk down to the PC and where I have my UPS and surge protectors ...
2.) some bitter apple spray ... (I know you don't want to use it, but I've read lots of things about how it actually really works ....)