Note that wirewrap used for consumer TV and audio off-board connections typically had a much larger square pin/post and wire diameter than wirewrap used for assembling prototype PCBs, which used thin 30 AWG silver plated Kynar insulated wire (aka: wirewrap wire) on 0.025" sharp cornered square posts, as shown at the Sparkfun link.
The tool *MUST* match the wire and post size. You *MUST* use a fresh wire end to rewrap a joint - you cant use what ever you unwrapped as the post corners cut into the wire to make gas-tight contact.
I suspect you may have some difficulty finding a manual wirewrap tool the right size for the wire and posts in your HiFi.
If you don't have the correct tool or enough spare wire length, the standard practice in the repair trade was to re-wind any turns that were insulated + a turn and a half of the bare end and solder it, clipping off the rest, but leaving a slight nub so you can unwind from the end if you have to desolder it. Once soldered, a post can never be re-wirewrapped. To avoid this hassle, it may be worth desoldering the whole post from the PCB to avoid disturbing the wirewrap joint(s).