From the CA department of justice website:
https://oag.ca.gov/firearms/certified-handguns/search
"Handguns Certified for Sale
As of January 1, 2001, no handgun may be manufactured within California, imported into California for sale, lent, given, kept for sale, or offered/exposed for sale unless that handgun model has passed firing, safety, and drop tests and is certified for sale in California by the Department of Justice. Private party transfers, curio/relic handguns, certain single-action revolvers, and pawn/consignment returns are exempt from this requirement." (Emphasis added)
However, a pistol transfer has to meet other California requirements -- no more than 10 round magazine capacity, for example; and must be transferred via an FFL. The P938 has a 7 round magazine, so that shouldn't be a problem.
"And it doesn't look like the Sig P938 is on the certified roster." ... getting on the roster requires the manufacturer to send (if I recall the number correctly) five of each, hmm, "catalog number" model to be tested. Sig-Sauer's web page shows five models of the P938, so the company ends up "out" 25 guns .. every five years, or sooner if they change some feature, which can be as trivial as the finish or color of the firearm. For some companies, it's not worth the bother.