Get some 18ga primary wire, strip back about 3", cut off about half of the strands, and twist the others up thin and tight. You can push it through the hole in the connector, and force the jacket into the hole to hold it in place. Cut the copper wiring off as flush to the connector as you can. Take what's left of the copper strands sticking out of the harness, and bend it flat against the head of the connector, away from the other row of pins. You don't even have to remove the mute wire.

Looks good to me....

Solder is just the "right" way to do things... It's a re-assurance that things won't come apart down the road...

Your's should hold up fine though... Just don't tug on it too hard...