First, order the new queen at once.
Queen is violated, because it produces only few eggs.
Let queen cells be there for the present .
When queen cells are capped, bees aprove strange queen very easily. When queen cells are open (larva) they often like to kill strange queen.
* Order a queen. It takes few days when queen cells are capped.
* Kill the old queen.
* Give new queen in the gage and look how bees react on new queen. If bees try to bite the box, new queen is in danger. If they do not react at all, that is the best.
But put the new queen under little screen cage with few bees. Let it be there. If bees do not attach against screen and bite it, it is Ok. Often queen lay eggs under the screen and it's approval is the quite sure.
Alternative 2) If you kill that queen and brake queen cells, bees will be very uppset. In that mental condition they may be aggressive against new queen.
I have foud, that when they have capped their own queen cells, it is very easy to give new queen.
It is also easy, when their virgin queen emerges, it is easy to kill and give a new one.