All K-frame Smiths should have the same cylinder dimensions, and the correct speed loader should work in all of them. Perhaps you have a speed loader for a Colt or a Ruger?
Your revolver is definitely a postwar (or post-Victory) M&P It is mechanically identical to the very late wartime Victory M&P models made with the improved hammer safety block beginning in very early 1945, designated as the SV-series for wartime production. A short time later, around the time that the S-series serial numbers changed to the C-series, the lockwork was changed to the "High Speed Hammer" short action. Yours has the old long action. The Model 10 designation was not adopted until 1957.