If you don't believe numbers meter gives you, and still want to run new wires to replace original ones, proper way is to not interfere with original wire in any way and just piggyback new wire on top. Remove only insulation and wrap new wire on top:
AND solder it on for good electrical conductivity.
Lack of solder is a very big problem. With crimped connections, it may appear to work in beginning. But over time with vibration and moisture corrosion, you'll end up with corroded and broken joints. Stress-riser from crimp accelerates this. Many planes have fallen out of sky from lack of solder.