For anyone reading this in future wondering how to get the Beige/Pink connector through, what some posters have said is true you do not need to remove the pins.
Once you've got to the point where everything is disassembled pull all leads through the base towards the mirror - except for the pink/beige connector lead
The pink/beige connector lead has two connections on the wing mirror side, one that connects to the mirror for heating and another white connector that connects to the rear of the wing mirror presumably to power the adjustment motor, pop these two connectors off (heater wires should already be off for you to have gotten to this stage anyway). Once this is done you just pull this wire out in the opposite direction to the other wires, through the mirror towards the base.
This is for non auto-fold mirrors if that makes a difference