IDC isn't up to the job, quite honestly. WMS should never have used them in the first place for voltage supplies, especially GI. I always go with Molex ones, Trifurcon crimp pins are the best if you can find them, but a lot of the heat in those connectors seems to come from the push-fit of the wire itself, rather than the pins - the normal single wiper type will work too.
Removing the other side of the connector is easy, but you will need a desoldering pump or proper desolder station regardless of method used - or braid if you really have all the time in the world to struggle with the stuff.
You can either desolder all the pins and remove the connector whole, which requires a desolder station to do safely (too easy to leave solder in place with other methods, resulting in pulling the pads and traces up), or remove it one pin at a time if you don't have one. Just heat each pin in turn from the back, and when the solder has fully melted, pull the pin from the front with pliers. When the pin is so hot the solder has melted, it'll slide through the plastic connector pretty easily. Once the connector is out use a solder pump to clean the holes.
When it comes to fitting the new one, remember to key it if appropriate for the connector - by either pulling the pin entirely, or clipping it at the base. If clipping it be aware that you're cutting pretty thick metal and the offcut will launch into your face if it's in the way, so be careful