If you have the tool and the connector pin into the button is the same type as the connector pin into the car connector you should be able to follow the wire into the button, take it out of the button connector, follow the other wire out of the button, remove that wire from it's connector at the car end and insert the first wire.
Is there a reason this would not work?
EDIT: tools like these stop you from boogering up the connectors and pins...
http://www.unofficialbmw.com/all/ele...tact_pins.html
https://www.ecstuning.com/b-schwaben...FQMDaQod-wkFBw