Jeanette Isabelle's initial post about a custom survival briefcase reminded me that women's clothing typicaly has no pockets. Even EDC must be a bit more of a challenge, so a custom briefcase or equivalent may make more sense for women.

Blending in: for EDC develop a pocket system or carry what people in your profession normally carry. Students, support technicians, etc. usually have packs, bags,and cases. Business types have briefcases: soft-sided, hard-sided, shoulder strapped, even rolling. Everyone carries a shopping bag or box from time to time.

If it is BOB time, change into your travel clothing - with which a modest backpack should look appropriate. You are just a student or casual traveler who uses a backpack rather than some other kind of "luggage."