202193 is way too early for an actual Parker Skeet Gun.
A s/n 202xxx Parker would be circa 1922. Skeet became a sport in 1926, so the 202xxx gun was never a dedicated purpose-built "skeet gun."
By the way, the game was called "Skeet" after a naming contest in National Sportsman
magazine, where the editor and inventor of the game pronounced Gertie Hurlbut of Montana, the $100 winner for suggesting what she said was the Scandinavian word for "to shoot." But afterward, National Sportsman
readers of every Scandinavian nationality disclaimed the word "skeet" as having anything to do with shooting a gun in any language or dialect.
In my research I found the original two-page center-fold contest entry form in a 1926 copy of National Sportsman
, and I noticed when I turned the page there was a very conspicuous title: "Skeeters..." to an article about mosquitoes. And I could picture in my mind's eye how a Montana housewife came up with the winning name...
I can close my eyes and see her now, trudging to the outhouse in the days when toilet paper was unknown in the boondocks, and especially Montana. She had with her the magazine her husband had just said he was finished reading, although her interest was not to read about hunting, fishing, or shooting. When the time came she started to tear off a page in the middle and noticed that $100 (a king's ransom in MT in 1926) could be won if she submitted a winning name for some game she knew nothing about...and then she saw the word "Skeeters..." leading into the article on the next page, and all the rest is history.
The game of Skeet was named, euphemistically, after the world's most annoying insect. EDM