I carry a couple knives for EDC. I've got a Leatherman Charge in a belt sheath on my right hip, and I've got a folding Spyderco Delica in my waistband, just to the right of my lower back.

Given your scenerio with my right hand pinned down or broken, I have a tough time reaching my Leatherman, but it is perfectly easy to reach my Delica.