Why not just use special blindfolds, i.e. completely blacked out goggles, provided by the competition holders. Then, they could be checked via a flinch test (make a punch gesture towards them, to see if they flinch - they shouldn't if they can't see)
Also, I recall someone posting a device that goes between the cuber and the cube, they put their arms around it, so even if they removed the blindfold, they couldn't see.
Dennis, I'd think you could understand why someone might not want to hold a piece of paper for your 16 cubes. It's a little more than a couple of minutes.