I unplug all the wires from the harness, remove the cables from the controls, then remove the handlebars and controls from the bike. Once that is done I carefully pull from the control side as I push from the part where wires are exiting. I also squirt a lot of wd40 down the bars to help it along.
When I am done I cut a hole in the bottom side of the controls and wire the bars externally with my new bars. Internal wiring is clean but it has no place on a daily rider, it shouldn't take half a day to change a set of hanndlebars!