First, you need to know how to remove solder and resolder well enough to proceed.
I won't answer your question directly, because mine will be just another opinion. I will say you can't disregard the quality of the wire you're replacing. You want to be very careful not to replace wire with worse electrical properties than what you replace (e.g. resistance, capacitance and inductance). I'd strongly suggest you measure each wire you remove for all these properties and not replace them with anything that has worse values of these properties. What is worse? That might be a separate thread. We'll see.
I won't answer your question directly, because mine will be just another opinion. I will say you can't disregard the quality of the wire you're replacing. You want to be very careful not to replace wire with worse electrical properties than what you replace (e.g. resistance, capacitance and inductance). I'd strongly suggest you measure each wire you remove for all these properties and not replace them with anything that has worse values of these properties. What is worse? That might be a separate thread. We'll see.