I agree with almost everything you've said
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I do suspect there are guns SO small that they could be confused as toys or something and lack intimidation value. NAA minirevolvers come to mind, some of the .25s. You're safest with something at least the size of "James Bond's gun" (PPK) or a snubbie .38.
I also think you're not paying attention to how the intimidation factor is related to YOUR obvious willingness to do serious mayhem if needed. The weapon doesn't intimidate so much as the guy (or gal!) holding it. Put another way: I've backed down dogs on several occasions and I'm quite sure they were too stupid to know what a knife was...but they understood my body language and lack of fear just fine.
Basically, intimidation (and backing the opponent down) is something that happens when you're NOT bluffing, and while welcome if it happens...if not, you're fully prepared to do mayhem. There should be no transition from "oh hell, the bluff didn't work, better get ready to fight"!!! Rather, the fact that you're ready and about to bust open a can of wooparse is what causes the violence to be unnecessary because all you can see of the opponent is their fleeing backside.
Understand, such chase-offs are welcome as hell! But they're not what you plan for, they happen because you fully planned to put the opponent in a blender and hit the "puree" button.
You've missed something else, too. The knife
. As a cop you think in terms of baton and gun. Civilians can carry knives most places and they have amazing intimidation value. Moreso than a baton, I think. The closer you get, the more deadly a knife is and harder to block...and they can kill even in untrained hands.