I'd go out of my way to attend a no request night. I've danced to songs never before experienced, simply because I was all ready on the floor surrounded by people. Its not that hard to find the rhythm. Not only did this make me feel fuzzy on the inside, it also deterred the creepy guy from pursuing me further, since he was at an utter loss of how to dance to it.
Now, if you wanted to be smart-asses, you could provide black request paper and a black ink pen to write them down with...You'd only need a single sheet to last you the entire night.