Disconnect the wires in the headlight bucket, don't cut them.
Pull the bars, unscrew the controls.
Lube (heavily) the inside of the bars along the wires and gently push them through the center hole in the bars, then gently tug from the control side (grabbing the wires, not the controls). Move them 1/4" or so at a time until the wire leads disappear through the center holes, then pull gently.
Spray more lube if you need to. It will clean up later.
Then decide if you want to either notch the controls and run the wiring externally (easier) or try to thread them in your new bars. If the latter, drill appropriate sized hole for wiring, make sure you file the inside lip smooth (otherwise it will cut the housing on your wiring and you will have shorts), tie fishing line (or something equivalent) around the end of the wiring with a weight (a nut, e.g.) on the far end, and dangle the thread until you see the nut in the hole in the center of the bars. Pull it through, then slowly push/pull the wiring through the hole until your control is seated.
No need to redrill the hole for the peg inside the control -- I delete them and have never had a problem with my control twisting on the handlebar as long as it is tightened down enough.
If you are notching the controls, hold the control in a vice, get the wiring out of the way, and have at it with an angle grinder until you have enough room to run the wiring on the bottom side of the control. File that down as well so it won't bite into the wiring.
Piece of cake!