Don't Panic!
A day featuring empty space simply has to be intergalactic (aka universal) in scope. They say that most of the universe is empty space, so it makes sense to have a day devoted to the awareness of that space.
But that's not the only empty space of which you can be aware. Look around you. Isn't most of what you see (not matter how cluttered the room is) really empty space?
Even most of an atom is empty space when you get right down to it. That means there's more empty space around you than you can even see. (I think.)
Space is known as the final frontier, which, when you think about it, doesn't really make sense. But who are we to question William Shatner? (Do you have photon torpedos at your disposal?)
There is one problem with celebrating Intergalactic Empty Space Awareness Day.
What is an intergalactic day? Even on the relatively close world of Mars, they use Sols, not Days. Who knows what they use on other planets? Even if they use Days, how long is that day compared to a Terran day?
Don't forget your towel.