Think about your position for a moment where "I can avoid a hammer, a bat, a screwdriver, and more than likely a car if someone is coming towards me to do harm. I can pick up something to shield myself, dodge, or run" Any of those items can be just as deadly as a person shooting a firearm. In some cases, more so.
If someone were to threaten me or anyone else legally carrying with any of the deadly weapons you describe, the outcome for all involved will likely be better. If a person carrying is forced to draw on someone wielding a gun, hammer, bat, knife, or anything else that would make them fear for their life, the attacker would likely understand that they need to turn around and forget the whole idea. At least that is what I would hope for. According to police, there are incidents in the area quite frequently where someone legally carrying uses their weapon in this way, and avoids any kind of devastating results for either. It's just not reported on. Why not try talking to the pros - the local police and sheriff's deputies - and see what their position is on CWP holders carrying. You might be surprised.
Stand there with with "something you picked up", and the outcome probably wouldn't be as good.
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