I'm exceptionally happy that you are not the one making the decisions on these rules then. You appear to not have put much thought into this at all.
We already know what happens in a world completely bereft of firearms, it's called history. And history is dark and brutish for much of it, until very very recently. Firearms are but one of many technological advancements human society has achieved that has brought about an end to the dark and brutish existence we lived until now. Why, you might ask?
Quite simply, eliminating firearms returns society to a situation in which defense is only possible through literal force of arms (e.g. the force you can exert with the arms attached to your body) which greatly enhances the power of those who are physically fit when they behave in a brutish manner. In your world the old, infirm, meek, physically unfit, and women have no effective way to defend themselves. Self-defense becomes the hallmark of only the strong, and something which is a far bloodier and less sure affair.
Spare me your world, because I have been a student of history and I see what that world is like. I like the world I live in now, where I can be reasonably assured that I will not be attacked by someone simply because of my small stature and have the legal and practical means to defend myself if I am.