Ok, it is not a DIY tutorial video but you see all components to build a complete new cable.
I use nothing from the original cable! The inner copper wires from original cables are thick and not that flexible.
The copper wires I use are thinner and more flexible (linked in the thread).
Stripping is a good alternative if you would like to keep it simple. And of course really better than original.
If you could solder, it is also possible to replace the inner cables and solder the cables direct to the pcb. That is good, if you wouldn't change your mouse/cable combination.