You should inspect the queenless part of the AS after 3-4 days and remove any further emergency queen cells which have been built which the bees will have done if there were any eggs present.
Once done, the advice I have read is to leave alone for several weeks. One word of caution though is to heft regularly and super them if needs be. I've ended up with a honey bound brood box where the newly mated queen has been unable to lay and the colony has swarmed.
Also a good tip to 'label' the QC if you haven't, using a drawing pin in the top bar of the frame, in line with where the QC is on the frame. That way you can recall which you decided to keep, and it's a reminder not to shake the frame.
EDIT: Also some would advise switching the queenless colony to the other side of the Q+ colony after a period (I forget quite how long, will be in a book) to draw any newly flying bees off into the Q+ colony, to reinforce the bee's sense that a swarm has happened.