No, DO NOT USE A SHIFTER ON THE OUTER RING.
I've posted before about the best way to straighten these. If you use a truing tool on the outer steel surface you will not remove the warp, but may put a twist into that band. They are not rigidly attached by the rivets and can move back and forwards slightly (about 5mm)
To straighten one of these rotors, identify which rivets are closest to the warp and apply gentle pressure to the rivet and aluminium carrier. I'd just use your hand. They don't take much pressure to straighten as the aluminium is fairly malleable. The steel band will follow the new shape of the carrier.
If you want some fun, try truing them so they don't rub on Shimano 4pots. There's a certain lack of tolerance involved. I think there's around 0.1 - 0.2mm clearance between pads and rotor. It took me a good half hour to get it right, but they've been right ever since (approx 1000km)