Re: Combining small nuc with larger possibly queenless hive
You can just put it in the hive, so long as the hive is queenless and does not have laying workers. Set the queenless nuc up next to the hive so the upper levels are even with each other and remove the lids. If one is queenless, the bees will move from the queenless hive to the queen-right hive. What you said about caging the queen and setting on top bars of the hive also works, the bees will tell you if they need a queen or not by how they either pay attention to the queen or try to kill her in the cage.
20+ years, raise my own queens, feed when needed. I treat, but have not perfected varroa management yet.