This method (storing queens in cages) is called queen banking. It is not generally advised as it interferes with the normal mating process for virgin/emerging queens, and for mated queens some beekeepers say that it affects the long term health of the queens.
If you have a bunch of cells and colonies that need requeening I would probably:
catch/kill the queen that is to replacedInsert the capped queen cell into the hive that needs requeeningLet the queen mate and begin laying in situ.
You might also consider making up a few two frame nucs, with just
enough bees to keep the queen cared for until you can confirm she is mated.
Remember, old queen killed by dropping them in alcohol (vodka!) make excellent Queen Mandibular Pheromone (QMP) lures for enticing swarms in the spring.