As far as I can determine, the company only used the term on the Model 1903 Hand Ejector. I can find and do not recall ever finding any other S&W models outside of collectors books, using that term on anything else . Of course I only have literature up to the 1950s. The first use was the Model 1896. It appears in the 1900 catalog and is named .32 Hand Ejector, Model 1896. My 1952 catalog still calls the I frames 32 Hand Ejector.
Roper and McHenry's 1958 book only uses the Hand Ejector term for the I frame 32, so it was not until Roy's book from 1966 did the term get general usage for almost all solid frame Smith & Wesson revolvers.