You CAN wear a cocktail dress, but it needs to be a dressy material (absolutely no jersey, for example; I'd probably also stay away from ponte personally) and look "evening" (so not something you'd wear to a business formal event). I would probably choose a dark color as that is more evening and dressy looking; black is always safe. I'd wear it with sheer black hose and dressy accessories.
Also, how conservative do you think this event is going to be? Like, really stuffy, or could you do "creative black tie"?
You could try Rent the Runway or similar if you don't have anything in your closet.
And to Elly's point, my husband owns a tux and wears it to a lot of events. I've never felt inappropriately dressed next to him while wearing a short dress. Admittedly most of these are black tie optional or creative black tie type affairs.