Hi mill3nia........What I believe your Grandfather had there is a ".32 Safety Hammerless". Some refer to it as .32 Lemon Squeezer or a .32 New Departure.
The concealed hammer with a "grip safety" design was a definate switch up for Smith! 1888 to 1937 (depending upon 1st, 2nd or 3rd model)....Given the partial seriel # you listed, it MAY be a 1st model (1888-1902)!
Story has it, that a youngster horse-assing around in those early Smith years latched onto a hammer style and gave it the old pull back and......kaboom. This might be what drove Smith to the Lemon Squeezer design.
Odds are a member here (or several) can shed more light on your old Smith. VALUE ....we all know how that goes, all depends on who would like to have it!!