Well, personally, I carried a brace of Ruger 22LR Target pistols, shouldered holstered, when I was in combat.
But what does that have to do with a full Regiment of 1500 soldiers? Mostly armed with Springfield, Enfield or M1 rifles.
Company grade officers with M1 Carbines. Weapons platoons with 50 cal. MG, Mortar platoon with 60 or 88mm. One BAR per squad. Perhaps the Regimental Commander, if adequately inspired by Gen. Patton, might carry a brace of 45 Long Colt Revolvers, Ivory handled, not pearl as the biased, ill informed media reported (nothing has changed.)