How well does the belly band method secure safeties and triggers as compared to a holster? As long as it's secure, the P938 fits well. If not, you might want to go for something with a longer or heavier trigger. Sig P239 is a nice gun but kinda big and not great capacity. I also liked the CZ PCR suggestion, or a CZ RAMI.
Beretta PX4 .40 S&W - Beretta 92FS 9x19 Para - Rock Island Armory GI 1911 .45 ACP - Colt 1968 Detective Special .38 Spc. - Ruger LCP .380 ACP - Daniel Defense M4V1 Carbine 5.56x45 - Alpine Industries M1 Carbine .30 - Steyr-Mannlicher M1895 8x56 - Ruger 10/22 .22LR - Remington 870 Express Tactical 12GA - 1943 Izhevsk Mosin-Nagant M91/30 7.62x54R