Is it permissible for my father to speak of the need when proposing on my behalf to a girl without reciting the Khutbat al-Hajah?

There is no harm in not starting with Khutbat al-Hajah (the sermon of need) or any other sermon when going to propose to a girl. The marriage sermon (Khutbat al-Aqd) is not obligatory; rather, some jurists have deemed it recommended, and Imam Malik held the view that a shorter one is better.