Once a trace is delaminated, you can replace it by jumpering with a wire. I use 28 gauge wire-wrap wire for that purpose. You can flat-wire directly to a trace after first tinning it. Or, you can solder to a pad. Best to hold the wire steady with a clamp or clip while soldering.
Fine wire is easier to solder with a minimum amount of heat.
I would try to avoid desoldering connections to a printed ckt board. The heat required to desolder is likely to be too much for the traces. Better to just snip the original wire or component from the the board, and haywire a new wire to the old connection.
Doug