Very Aggresive Bees - Stinging on Sight - Requeen Advice?

I’m new to bees and also have a hot hive, not quite as aggressive as yours but 50 plus bees head butting the veil every time I do a inspection. Regardless of how much smoke I use and how gentle I am they act the same and I have 10 or so stings in my gloves at the end of the inspection.
I have ordered a new queen for later this month, my plan was to kill the existing queen, leave them queenless overnight and then introduce the new queen in her cage the next day.
I am also interested in increasing my hive number from my current 3, I have had it suggested putting the current queen into a nuc with just one frame of brood and another of honey quite often significantly quitens them even once number build up again.
I’m going to try it as will only cost me a frame of brood and if they reject the new queen I can put the old queen back in, leave them until spring and try again.