Cut off the connector you don’t need, you can leave some wire in case you ever need it for some reason, or you can cut out close and just toss it.

Cut off the one you do need, with lots of slack, and then splice on to the freshly cut wires (hopefully with solder and heat shrink.)

Connect it up and move on, hopefully you’ll never need to think about it again.

If you still really don’t want to do that, you can try pushing the pins out. This might help: youtu.be/0G7iIwfuaJ8 and this youtu.be/BbXX32X-Hkc

The paste might be dielectric grease to keep moisture out.