flanman:
You have a .32 Hand Ejector Model of 1903 1st Change, manufactured between 1904 & 1906 in the serial range 19426 to 51126.
In the early days of the Hand Ejector (swing out cylinder) models, each time S&W made a minor change to the design it received a numerical change designation. So first change, second change, etc. These days, with model numbers instead of names, there is a -1, -2, -3, etc suffix to the model number. Some guns such as the Model 60 are up to -15 or more.
Major changes meant a new model designation. So the .32 Hand Ejector Model of 1903 (or Second Model) replaced the Model of 1896 (or First Model) because it was essentially a new design. The Third Model in 1917 had a major internal change in the form of an internal hammer block safety. In between the 2nd Model & 3rd Model there were 5 minor changes to the design over 14 years and roughly 243,000 guns. These differences are basically irrelevant except for hardcore collectors wanting the full set of variants and for gunsmiths who may have to work on the gun and need to know the details of the changes and the serial ranges to find a compatible parts gun.
For the purposes of the average shooter, the important things to know are a) is their gun from before or after S&W started advertising their products as safe to use with modern gunpowder instead of blackpowder in 1909, b) is their gun from before or after the introduction of heat treated cylinders in 1920, c) is their gun from before or after the introduction of the positive hammer block safety in 1944 & d) is their gun from before or after the change from the small I frame to the slightly larger J frame in 1961.
Your gun predates all of the above.
Therefore:
1) Modern J frame grips will not fit your gun, you need to either contact
http://www.gunpartscorp.com/ to see if they have a good second hand pair or do a google search to find the manufacturer of reproduction grips.
2)Lacking the internal hammer block safety, if the gun is kept loaded the chamber under the hammer in your gun should be left empty. If loaded and dropped on the hammer it could fire.
3) As your gun predates heat treatment of cylinders and S&W claiming their guns were suitable for smokeless powder, if you choose to shoot your gun stick to lead factory ammunition or handloads that are no more powerful than factory ammunition. If you handload, consider using a blackpowder substitute load such as Goex instead of gunpowder. Blackpowder is slower burning than smokeless gunpowder, so the pressure peaks slowly. This puts less strain on the gun. Unless you know what you are doing, don't reload with blackpowder though.