Cord on my HRAP3SA shorting out, what do?

What the title says. How do I go about fixing it? I don’t have the money nor the desire to buy a new stick just because of a short.

why not just solder on a new usb cable?

Replace the USB cable.
Any USB cable will do, as long as it as the Type A USB male end as the other end will more than likely chopped off.
It does not even require that stupid disconnect that XBox 360 Controllers have.