I'm going to have to say no.
The reason is that some people have already made their plays for today and would not have had the opportunity to pick the CHW if I opened that door now. Sure, we could give them a chance to change their picks but that would cause even more problems since not all of them would see this "change" before the game started. So we can't really do that.
I realize this isn't the greatest situtation but, I can't see modifying the rules now without causing even more issues.