I have no experience with the Sig P938 however I do have a Kimber micro9 in 9mm of course. And it's fairly similar in size, weight, action and so on. According to handgun hero.
And I'm a big fan of the 1911 platform, single action hammer guns. But I must say I just never got real comfortable with the Kimber as my EDC.
The recoil was just not good for my fairly old hands. The beavertail started digging into the web of my hand in short order. Making any long term range/shooting time no fun. Plus the 7 round limit?
I went to the already mentioned Sig P365 and have never looked back. Way more comfortable to shoot, easy follow up shots, higher capacity, and so on.
I highly recommend it for EDC. And I was never a fan of plastic striker fired guns either.