I had to solve this problem when I was a pilot/reporter for a TV news station, listening to five radios and my cue from the anchor. What worked best for me are Brimz. They don't have any arms at all to go under your headset - they just attach to the brim of your ballcap. Swing them up and they go flat against the visor, swing them down when you need the shade, and they don't do anything to mess with the seal of your headset.
I've still got a set on my uniform cap, because I'm too lazy to fish a set of sunglasses out of my flightsuit pocket.