nice that you have found the cause,
if the thing is on the cord :
make really sure no other wires are damages because in that case you could create a short when you ll squeeze everything back together.
if you have a spare usb cable mybee you can have your friend use it a a replacement for the damaged cord, so have him soled the USB spare cable in palce of the former cord.
or if it located close enough to the stick box which i highly suspect just cut the few cm of coord where the cut is and solder back the cord on the PCB at a point from where you are sure the cable is healthy.
if you are sure that the only damage line is the red one, you can do what he told you mash the too extremeties of the wire together and binf it with tape, if you wan you can add aluminium foil around the naked splitted wire before the tape to reduce the chances of loosing the contact when the cord is being moved.
Now if i am all wrong and the wire is damaged inside the box , you can still apply the solution where you desolder the cord, get rid of the damaged part and solder back the coord from where it is clean, or you can fix the problem as you described, in which case you will also want to add aluminium foil around the “tended wound” and then tape it VERY thouroughly to avoid any possible chance of a short.