If I don't have enough cap space to cover my draft picks, will I be able to make the necessary cuts to get back under the cap or will my draft pick contracts be voided?

You have all of late free agency to get under the cap, you won't be able to trade until you are under the cap.

Thank you. That's all I needed to know.

I had no idea you couldn't do this. Even if it helps decrease the cap?

pretty sure it won't go through if you are still over after the trade would process, if the trade would put you under the cap then I'm not sure.