DIY: Aftermarket cruise control install
There's a method (using a push pin) to remove the wires out of the connectors. And once out they can just be pushed back in. I found it was very easy to remove the wire from the connector. Just follow the instructions, if you want to go this route.
So does the white connector fit into the existing socket? If so you can just pop out the green (ground) wire out of the old connector and put that wire into the new white connector.
If it doesn't fit, you could move the black connector over onto the new switch. Leave the ground wire intact on the black connector, remove the red and white wires from both connectors, and then move the black connector onto the wires on the new switch. (Per the pictures wires are green (ground) furthest left, then red, then white.
If it doesn't work, you could always put the white connector back on and return it.