In fact I think women shouldn’t even be invited to the wedding (other than the kallah)
You can go even further… you don’t need the kallah there either. Have her appoint her father as a shliach to accept kiddushin for her. Then she doesn’t have to be there at all.
After the wedding, the father can then drive the kallah to her new husband’s apartment (thus completing the nisuin) in total privacy and with complete tznius. 🙂