Ooooooh Firstclass congratulations!!! finally, your dream bag!!!
06 leathers were spotty. Believe it or not, yours isn't too bad! I know it's not what you expected, but give it a shot anyway. The leather on my Ink day was so unappealing at first, I couldn't decide whether I wanted it, and now it's gotten softer and lost some of the shine, and I never ever wish it were different!
The stiffness of the leather makes me less careful than with the other bags, and it's somewhat a relief to have a Balenciaga that I'm not afraid of damaging.
I would recommend holding off on conditioners and see how much happens just with use. Give it a few weeks, and then condition if you see fit.