R’ Moshe Feinstein ZTL mattirs shaving as discussed in the Beard thread.
Many chashuv yeshivos require their bachurim to shave year-round (not during sefira and 3 weeks). I have heard that some of these same yeshivos will mattir (and even recommend) shaving during 3 weeks and sefira for first dates in order to make a good first impression. (I don’t know if this extends to 9 days or shavua shechal bo)