Why not just put a sticker on the hand dryer?
That's just as good of an ad for something people will see for only five seconds or so (assuming it is one of the good hand dryers that blows like a jet engine to dry quickly) there's little point in moving video.
And if you are putting a sticker on the hand dryer, why not on the door, the wall, the inside door of the toilet, on the mirror, on the countertop, and on the ceiling in case someone looks up to avoid ads coming at him from every direction?
If some really thinks an ad on the hand dryer is going to pay the cost of the video screen and electricity to run it, surely ads all over the room will be even more profitable if they don't have the cost of video screens?
When you want to change the ad, just wait for someone to peel the sticker off because its there, or put a new sticker over the old one? Unsightly, you say? Pretty sure that video screen will be unsightly from people shaking their hands as they approach the dryer and having it cleaned with the same rag that was used to wipe down the mirror, countertop and sinks!