...that S&W Bodyguard 380 would fit the bill except for one thing: it is one of the ugliest guns I have ever seen. No offense to those of you who own and love one, but after owning the most beautiful handgun ever made (Beretta 92) I'm spoiled for life.
Prefer Beretta styling? I have a potential solution for that- find yourself a Beretta 70S.
It's wider through the grip area than the LCP or BG380, but this potentially aids controllability. It's a single-action pistol with a thumb safety, like a SIG P238, but can be found much cheaper. The main issue is that they've been out of production for a few decades, so they can be tough to find, as can spare mags; also, some shooters greatly dislike the peculiar crossbolt mag release.
FWIW the Beretta 70 (no "S") aka Jaguar is similar, but it has an alloy rather than steel frame, and is .32ACP or .22LR rather than .380ACP; some early-production 70's also have a queer crossbolt safety. I mention this because you'll sometimes find a 70S incorrectly labeled as a 70 and/or a Jaguar, or vice versa, although this is technically incorrect. When browsing online classified ads, I typically search for all 3 names (70, 70S, and Jaguar), then check the slide markings and safety type of the individual pistols.