Phil, hard to call it a Skeet Gun without the SKEET IN/SKEET OUT markings on the barrel flats, a PGCA letter or perhaps something from G & H. By the Remington date codes on the barrel flats it was made June (P) 1939 (H) and was in March (A), 1945 (PP) for repair (3).
While the Parker Skeet Gun was usually shown in the Remington era literature with a straight grip, there was the choice of a capped full pistol grip, half pistol grip or straight.
Parker Skeet Gun 1938 catalog.jpg
SKEET GUNS 1939.jpg