How many soldiers did carry handguns?

It is true that the W-SS used a lot of Browning HPs', I couldn't say, based on photo evidence, that they were used in greater numbers than Lugers by the SS. I don't believe that widespread use (on a real large scale) of Brownings HPs by the W-SS began before about 1942. It is certainly true based on confirmed production numbers/dates that the single most widely used pistol in the German Military (as a whole) was the Luger,P08 until at least into 1944.