No, don't do it. As much as a Sig fan I am, the P938 is about the same size as the P238 and is way balistically superior. Why and when would you carry a P238 over your P938? The G20 is a max firepower gun and complements your P938. FYI, my P938 is my favorite EDC gun. I too have a G20 and its about as good as it gets for max firepower in a pistol.
I am not a Glock fan but the G20 is the exception in 10mm.