KSCCTrainer:
Unfortunately the Standard Catalog of S&W doesn't give a breakdown by year on that model.
The .32 Safety Hammerless 3rd Model was manufactured between 1909 & 1937 in the serial range 170000 to 242981. The earlier 2nd Model averaged roughly 10,000 guns a year, so its likely that your gun dates to around 1910 to 1915.
The only way to be sure would be to obtain a factory letter from S&Ws historian, Mr Roy Jinks. The letter costs $50 (he has to manually research the original shipping papers) and the gun is only worth around $125-$185 in that condition per the Standard Catalog of S&W, so its probably not a worthwhile option unless the gun has family history.
The third model was manufactured after S&W started advertising them as suitable for smokeless powder, so it should be fine with current factory ammo.