Here's what you've got . . . a 4 1/4" barrel Model 1903, fifth change from around 1920.
My 4 1/4" barreled M1903, fifth change (serial # 2459XX) was made in 1916. The .32 S&W Long cartridge can be quite accurate when you find the right load for your revolver too . . . though the tiny sights on these Hand Ejectors make it more challenging to get a perfect sight picture.
Here's my 'new" (to me) 1903 Fifth Change. They came in both blue and in nickel offerings, with either black rubber stocks (the most common found) or with wood stocks.
Hope this helps . . . and here's mine . . .
And yes . . . you can shoot the snot out of these little guns if they are in fine condition. Here's a couple of targets I shot with it TODAY . . .
Distance, ten yards from the bench . . . five rounds into each target. Homemade targets are 1" black squares on white 3-hole notebook paper.
BTW . . . 32 Long revolvers are picky about ammo, so you have to find the loads your gun "likes." Case in point . . . here's the WHOLE target shown above.
The top two targets are Fiocchi 100 gr Wadcutter. My gun didn't "like" this load for some reason. However, the two bottom targets were a different matter, with the round nose bullets grouping pretty danged tight. I'm sure they would have grouped even tighter but it was hard picking up the tiny nickel sights in today's bright sunny afternoon!
BTW . . . the three big holes on the left side are from the homemade target's 3-hole plain notebook paper that I print my targets on.
PS: I'm sure your grandfather would be happy to know you are still shooting his special revolver . . . I know that this would surely bless me one day if my three sons and their kids will do likewise with my guns!!!