The official Walther history "Walther - A German Legend" says that "soon after the introduction of the PP and PPK, Fritz Walther tested the market with a model in 9mm Kurz [9x17 or .380 ACP]."
"Soon after" is not further explained, but in a comparison of 1933 and 1939 price lists a few pages later, neither 9mmK version is shown in the 1933 list, indicating they were not available in that year, though they were by 1939.
The 9mmK was never a popular cartridge in Europe, and was never standard issue with the German police or military forces. (The postwar 9x18 "Ultra" was an attempt to get more power than the 9x17 within a blowback pistol.)The Walther book indicates the 9mmK PP/PPK pistols were made "primarily for export, and most of them went to America" and that some 25 9mmK PP's were made for every PPK in that caliber.
Jim