My method is using a wire to bypass the whole trace. Scraping the solder mask and the heat from the soldering iron can stress the already damaged trace, and could lead to the trace lifting, at the solder time or in future.

Can you show with photos and explain what the trace did. For example, if the trace carried mains voltage to a relay then you should try to maintain proper clearances for safety.

I am trying to just bypass the damaged part, following the damaged track. However, is it sometimes hard, to get the repair wire to stick to the track, so it my be easier to bypass the track altogether and go pin-to-pin.

Interesting!