פירוש על קידושין 72:5

The word “hand” is used in the context of the sotah offering and the peace-offering. This allows the rabbis to combine the two procedures—in the context of the sotah-offering it seems like the priest is supposed to wave the offering, whereas in the context of the peace-offering it seems like the owner brings it. So the resolution is that they both do so together.

The word “kaf” is used in both the context of the sotah (Numbers 6:19) and the nezirah (Numbers 5:18). This allows the process used in the sotah to be applied to the nezirah. She too waves her offering with the priest’s hand underneath.