I like the costume, and don't really have any problem with the KK design (but then, I've never read anything of her in her socialite guise), but I do have two problems...
1: The wig. I thought we established that wigs were inconvenient things for crimefighters to wear back when Black Canary stopped wearing one? Anyway, if her actual hair color is red, why not just grow it out and wear it in a ponytail or something in her civilia identity? A different hairstyle can be very effective in concealing ones identity - I've often come across friends who've changed hairstyles or hair colors since last I saw them, and there is ALWAYS a period of two or three seconds where my brain goes 'what th',,,? Who IS this?'
2: The skin tone. I will grant you that blazing red hair and pale white skin is a very effective contrast, but A: it's been done before, and B: white skin and red lipstick immediately remind me of the Joker or Harley Quinn. It's kind of their visual trademark, and it could be a little jarring to see someone else doing the same thing.