I am painting a playhouse for my kids and made a mistake on the shutters. I wanted the outside black and the inside white, but accidentally painted the inside already with black satin spray paint (the outside is still coated with just white primer). I'm limited on white primer (yes, I know it's only 4 bucks to buy another can of it), but have plenty of the white paint. I also have plenty of gray primer (spray can).

Can I just paint the white directly over the black (I have enough to do 20 coats if needed, since it's really a small area)?
Can I spray gray primer over the black, then paint white? Or should I really do the whole shebang: sand, spray white primer, then paint white?

Thanks!