Question Repair wiring insulation?

That's just a standard USB2 cable on there. 4 wires, nothing fancy. If the wires are still fine, you can use basically anything. Repaired a cable the other day with regular sticky tape.
You could use shrink tube, electrical tape, other tape, even hot glue. Or put on a different cable. Just depends on how much of an effort you want to make and how nice looking you want it to be.
 
Replace the cable if you can. 4 wires will be connected to the pcb in the plastic housing. 2 will be power, 2 will be data. You can get strain relief grommets from electronic hobby shops for pennies to make the job look pretty.
The link is to a picture of the usb connector and wiring. Check this against your existing wiring.

https://www.electroschematics.com/wp-content/uploads/2010/01/usb-wiring-connection.jpg

It’s a 10 minute fix