''Cannot find the queen''
Often an exaggeration or an excuse for not really trying.
Split the frames into two boxes. Queen will be in one of them, yes?
Which part is calm and settled and which part is agitated and noisy?
Now you know where the queen is, don't you? Wasn't difficult? In fact quite easy!
As long as she is not on the frame with the supercedure cell, your problem is over (at his stage).
You should now have two nuc sized potential colonies and can split/reduce the queen's share further by the same method, although it may be a little more difficult to isolate the queen to just a couple of frames.
At this time of the year and it being your only colony, I would certainly try to keep the queen going in a nuc, at least until the emerging queen is mated and a proven worker layer. And preferably until you can assess the temperament of her offspring! What you do then is up to you.
RAB