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The standard 9mm round is the 115gr bullet weight Billy. I would zero the pistol according to your preferred carry round as different weights and velocities will zero differently.
I have an early P938 that basically only fed 124gr or higher reliably. After going back to Sig, it will handle any of the 115gr, and the recoil is milder. I bought a second P938 earlier this year, and it will handle even Sinterfire 90gr without a problem the recoil is mild, but velocity is high, so still packs a punch. When traveling, I use the +P 135gr. Both handle the Corbon +P 115gr and I like that load too.
The only way to really know is to try different ammo until you find what it likes. That said if it does not provide "self defense" accuracy with any good commercial ammo I would be surprised
All of them I've shot ( I shoot many pistols just because my students can't hit with them and think they are broken) the bullet impacts right on top of the front sight with the 115 or 124 grain bullets. I've never seen one that wouldn't work though. Grip is usually the culprit.