You could add a frame with fresh eggs on it instead, but you will still have to juggle the boxes. Equalize the two hives giving the queenless hive a frame with eggs. However that puts you 50 days out for new bees....
I think one of the youtubers addressed this recently. Fred Dunn or Duck River.
For this combine I think I would do a newspaper trick and put the small one on top of the Queenless, leaving the supers in place. Rotate the boxes shortly after they have merged? (It is said the queen will not cross honey.) You would want to think about drones too if you are using an excluder (I think no excluder would be better temporarily).