Most plugs like this has a tiny clip on the pins to keep them inside the plug. Either push the tiny clip down and ease the pin out of the socket, or use brute force to get the pin out, destroying or bending the tiny clip, and bend the clip back afterwards so it will fit again.
When the pins are out you can solder the wires back on again.
Otherwise you could back-track the wiring, cut the AT connectors off and use some new of your own choice.
