Okay so it’s pretty simple to remove the pins from the connector and if you have a solder iron the wires are soldered into the terminal so it’s possible to remove the terminal heat the terminal to melt the solder and quickly shake it to spill the contents. Strip the insulation from the broken wire about 1/4” insert and resolder. The slide lock just pops out to the track exposing the terminal latches. Just be careful as they have become quite brittle. Insert a jeweler screwdriver from the wire end and carefully displace the latch. Because the wire has broken you might need to use another jeweler screwdriver and insert in the terminal you need to remove and gently push it out.
If you don’t have a solder pencil or gun I can send you a wire and terminal with a crimp terminal on the end so you can just replace the bad terminal. Just let me know what wire color you need.