I don't really think you can go wrong but I'd start Lee in the pen.
I'd probably need to see the player to answer that correctly but I think it's 10 HBD days like when you send them to the minors. Otherwise, owners would use that as a way to create extra BL roster spots. Blow up a pitcher, designate, call up another, blow up call-up, assign first pitcher back to BL roster. Ask 'motown in MG. He used the loophole for awhile and they closed it.