They want photo id and work info for screening? Or is there another way
I have to admit that, having known them both from earlier gigs, I didn't have to go through screening with them under their new incarnation. I'd suggest asking them if provider references, Whitelist refs, P411, or something along those lines would be acceptable. They're popular ladies - they can afford to play it safe.
I will also say that I trust them both to be completely discreet with any information that you give them. So if you show them a work ID, they're not going to be making a copy of it or memorizing your name and your company's name; if you give them your work info I'm pretty sure that they'll destroy it as soon as they verify you. So, knowing them as I do, I would not be worried about my hobby life intruding into my work life.