Welcome to the forums from the Wiregrass! You have a .32 Long Hand Ejector, Model 1903, 1st Change that was made around 1905. The pre-WWII .32 Hand Ejectors are built on the small I frame. Things like replacement grips are getting hard to find and it appears your hard rubber grips are quite worn to the point where the checkering is gone. If you take them off for cleaning, DO NOT pry them or you will break the bottoms off where the grip pin engages the grip panel to hold it in place. Loosen the grip screw and then push on the screw head to pop off the right panel. Then, you can push off the left panel through the frame. The serial number of the gun should be scratched into the right panel. Grips were hand fitted to the gun back then and the serial number on the right panel was used to keep the gun and grips together during the manufacturing process. If the grip serial matches the gun, the grips are original to the gun.
Congratulations on an early example of the S&W I frame. We don't often see the .32 HE in a 6" barrel. It should make a fine display.