I have a Hammerless Safety ("Lemon Squeezer"). I believe it's a 4th model. The serial is 117XXX
Assuming it's a 38 caliber. It would be a 4th model. Serial numbers ran from 116003 in 1898 to 220000 in 1907.
I would guess it to be within the 1st year of production but only a "letter" from S&W can verify that.
If it's 32 caliber it would be a 2nd model made between 1902 and 1909.