I have both S&W models 36 (Chief's Special) and 37 (the airweight version) with 3" barrels. They are not common, but they are out there. Both of mine were blessedly of C&R age, which was handy. I also have a strong preference for the older revolvers, because of the attention to detail that they exhibit.
If five shots is not enough, Colt made the Detective Special in a 3" version as well.
If CCW is a goal, I'd personally prefer a small-frame revolver to a larger one. And like you, I find .38 spl quite enough cartridge. Buffalo Bore makes a self-defense round that is loaded and charged especially for short-barrelled revolvers of a certain age, in which you wouldn't want to run +P loads.