If you go for a derringer, you should check the way it fires, any live chamber gun should not be used by someone who is not aware of it's shortcomings like a hard blow on an exposed hammer, ETC. One with a transfer bar controlled by the selector would be preferable. The small 22 mags with a cylinder are a good choice if handled properly, and are not limited to just two shots. But if it is open carry why limit the available reliability, knockdown and ease of target acquisition.
My CCP carry is one of two, a (high standard double nine 3" 22 Long rifle revolver. Absolute reliability, 9 shots less weight than a can of Vienna sausage, pocket size). Or a SW Military Police special 41 mag nickel plated with custom wood grips. The 41 has half the recoil of the 44 and 3/4 the knockdown.
My wife has a Llama Mini max 45acp 9 shot 4" it is almost like a Colt 1911 commander but has more shots. It has a lot of recoil for her but she can handle it with two hands and nobody will stand up for a second shot. I cut the end of the hardballs to spread fast.