The queens are not large cell or small cell, they are all the same. I have raised queens in large cell hives and small cell hives and the queens are the same, they can lay eggs in small cells or large cells.
Not sure I quite understand your question, but putting a particular queen in a large cell hive will not make it small cell you have to have small cell comb.
EDIT - Started writing before your post appeared Michael, sorry have covered some of the same ground.