or, you could buy a 3.5mm cable, cut off the one end and splice the two cables together,solder and seal with electrical tape or heat shrink.
if the cat just chewed the insulation and the wires are still unbroken and intact... just peel back the insulation sleeving... make sure the internal wire sleeves arent damaged. if they are, wrap them in some electrical tape. tape up the whole outside with electrical tape or use shrink tubing.
under $5.00 fixes generally assuming you have basic tools.