Looks like all the Standard Catalog of S&W gives is a broad range from 1911-1942 which covers serial numbers 263001-536684 of the 3rd Model .32 Hand Ejector.
Sorry, but there is no way for me to tell which year it was shipped from the factory, by looking it up in the book. Call S&W, or send off for a factory letter, its the only way to see if further info is available. Or maybe someone has a serial number close to yours that knows the details, that still wouldn't tell you what year yours was shipped in, which is all S&W has records on, not dates of manufacture.
"No free man shall ever be debarred the use of arms."- Thomas Jefferson