Not this hat. It seems to be thought controlled by Wo-chan, but doesn't seem to have any other special quality beyond being her equipment. It can launch fighters, be a gun mount, and carry pillows.
I'm becoming convinced it's actually a "Blink Ribbon", and phases in and out of the Prime Material Plane at random times to help it evade damage in combat.
Hence, as captured still-images in time, each frame has only a percentage chance of actually viewing Wo when her ribbon is manifested in our dimension.
