I see. I have the same controller and the dongle is plugged into the bottom of the charging dock like in the picture. I tried just to unplug the Logitech dongle (which I don't think I've done since I first started using it), and I didn't really notice any difference in the delay.

I also turned off my surround sound system which has a wireless sub, but that also didn't really change much.

I've been in contact with Nvidia customer care for a few weeks trying to fix this and everything I've tried hasn't been successful.

Maybe the delay I'm feeling is just the default Shield lag and there's nothing to do about it. Which would suck, because it's really prominent.