1. Don't solder in anything. It's solderless connectors (with the shrink tubing built in) or replace the wire. If the strands of wires are intact, how close is the nearest terminal, where you can carefully remove the terminal from the socket and slip over a piece of shrink tubing?
2. In this case, I'd probably carefully reshape the insulation for looks and apply a few coats of liquid tape so that it's as inconspicuous as possible. "Normal" electrical tape will look ratty after a few months in the engine compartment.
https://www.amazon.com/Permatex-85120-Liquid-Electrical-Tape/dp/B003ERU04W?source=ps-sl-shoppingads-lpcontext&ref_=fplfs&smid=ATVPDKIKX0DER&th=1