I only own and have only fired the K40. But, we're talking about tiny little guns here, and I think they can be a challenge, no matter who makes them. My opinion, based on my K40, is that Kahr makes excellent pistols of very high quality. I bought mine used and in fact it was a factory refurbished unit, and I had my share of problems with it. Those problems were all due directly to handloads that were most likely, in all cases, unintentionally well over maximum loads. Have had no problems since in shooting probably well over 5,000 rds. It is a very accurate-shooting pistol--for any size handgun.
There are really far too many things to worry about, IMO, to include worries about what might happen with your CT380. If it were mine and I didn't handload, I'd buy a box or two of something reasonably-priced such as Fiocchi, Prvi Partisan, or PMC ammo and see how it shoots. If it feeds reliably, then I'd buy as much as I could afford to shoot and practice with it. It took me about 1,000-1,500 rds to 'get good' shooting a DAO accurately and quickly from the holster. It may take you far less--I find the tiny little guns to be a real shallow learning curve: they're not easy, and progress for me only came as quickly as my weak hand and trigger finger figured out what to do with themselves. I don't think you can speed this process up much--it takes time.
Work in several boxes of whatever you intend to use for carry ammo over the months, as well, and get to know the little feller.
Every make and model of handgun out there probably has its share of 'horror stories', every single story accompanied by equal shares of "yeah me too" and "never had any trouble with mine". Work through issues as they come up, if they do. In the mean time, learn to master the weapon...and enjoy it.
I put the Trijicon sights and wooden grips on mine and had it MagnaPorted. To my great surprise, none of these improvements tightened my groups up at all.
Finally, I carry it. I don't tend to do that unless I have 100% confidence in the function of the gun. That confidence doesn't come from the brand name, the caliber or internet lore and legend.