I thought Deadshot started off with a tophat and waistcoat. If I'm mistaken and there's a cowboy story that I'm missing, please let me know where I can find it, because I'd love to read it. That might put the moustache into some context, too.
Anyway, I would be fine with changes to Deadshot's mask that let us see more of his face. Having a fully-covered face was fine for Rorscharch (possibly because the moving ink blots conveyed some feeling), but I feel like when you hear the actor's voice but can't see their eyes/mouth the whole thing feels kind of...Power Rangers.
I felt that way with parts of the opening scene of The Dark Knight ("Now I know why they call him the Joker"), too. That's also why I hope the sonar lenses on the batsuit won't make a return. Maybe it's just a matter of personal preference, though.
And I think that as long as we see Floyd Lawton as a chain-smoking scumbag with guns on his wrists who's indifferent as to whether he lives or dies it'll be Deadshot--even if the costume is changed.