These connectors can be a bit fragile if you pry too hard or too fast.
Here is one of the exposed wires. I already rewired one of the pins here.

So the first thing is to disassemble the connector. Some connectors have multiple plastic bits helping to hold in the pins. This one only had the big piece below. Gently prying on one little plastic flap allowed it to slip out.

Each pin has its own individual plastic locking piece that is part of the connector that holds the pin in. Pry it a little with one little flat head

and use another flat head to push the pin out the back. Be careful pushing it out and don't push too hard or the locking piece might break.

So now its out. Pry back the small metal flaps and take whatever the rubbery thing is called off and save it.

Twist some new wire together. Note that if you don't plan on soldering you should use more of the old wire and not twist the wires together like this.

Solder it. Put the rubbery thing back on. Clamp the metal flaps back on the rubbery thing and electrical tape or heat shrink it and its done. When you put it back in the connector there is only one way that the pin will go in so don't force it.

