P-08, S/N 6623 - Believed Military - Need Help Identifiing

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I recently received a P-08 from my father. He purchased it as a war souvenir at the conclusion of WWII while still US Navy officer. He was told it was a German officerâ??s sidearm. This may or may not be true. Iâ??m confident the collective expertise of the readers of this forum can prove (or disprove this). The pistol has a bright, reflective finish (stainless/chrome/nickel?) [frame & barrel] with black bakelite grips and a high quality tan leather holster. Frame marks include, â??P.08â?�, â??6623â?�, numerous â??23â?�â?? marks visible on assorted frame parts. On the right side of the frame is a tiny Third Reich emblem (eagle over swastika) stamp. The right side frame also has several other tiny stamped glyphs that I canâ??t interpret. The barrel is marked both â??6623â?� and â??881â?� with a Third Reich emblem stamp identical to the frame. Iâ??m guessing 6623 is the mfg. S/N. Any help in identification is greatly appreciated.