Khulʿ is a divorce of a wife who is not fond of her husband and has an aversion to him and gives him her dowry (mahr) or some of her other property so that he divorces her.
In a khulʿ divorce, it is a requirement that the wife’s aversion to her husband be at such a level that it is a threat to her fulfilling her marital duties.
Khulʿ seegha is applied by the husband, not by wife.
He says: I give my wife a khulʿ divorce upon accepting what she has given, and so she is divorced.
Hence, what you suggested, is not applicable.