Ha! Turns out I've already covered that situation, then!
I've carried some kind of bag since High School. Even before I got the preparedness bug I EDCed a couple of pens, notepad, lighter*, cell phone, Leatherman Juice, and a flashlight (along with the usual wallet, keys, etc.).
I had already added some bare essential PSK items, but when my AMK PSK arrived, I found there was room in the bag in a previously unused pocket to simply EDC the whole thing! I also stuck in a "micro-FAK" (just bandaids and antiseptic wipes), so with my normal EDC bag and a water bottle, I've already got the "away from my car" situation adequately covered for my own comfort.
*Nope, I don't smoke, but I'm sure I don't have to explain
here why I carry one.

(Edited to add: the full PSK is major overkill for anything I expect to encounter day-to-day in the city, but since it fit into my bag so neatly, I figured it was better to have it and not need it than the reverse.)