I have a smallish Eagle Creek bag that can be carried as shoulder-bag or waist-pack. I don't call it a "man bag" or a "murse" or any such thing because that makes it sound even gayer. I like the Eagle Creek one because its style is not effeminate with being overly-macho (cf the Maxpedition stuff). Also it doesn't look too expensive.

It has two main compartments. I keep one mostly free for utility use. The other half has a small first-aid kit, an emergency bivvy, headlamp, monocular, N95 mask, paracord and various other preparedness stuff.

I also have fairly full pockets, and I don't take the bag everywhere so I don't consider it EDC. It's not so much that I care what others think as it not being convenient.