There are disagreements about the exact date of first K-frame 2" barreled snubby's production, but for sure it was in the 1930s. However, there have been many examples of earlier frames, such as yours, which have had the original longer barrel replaced by one in 2". Of necessity because 2" barrels were not made by S&W prior to the 1930s, the conversion had to have been done later than that. If there is no SN on the barrel flat, it probably would have been done by some gunsmith outside the factory, as S&W stamped a matching SN on the flat of a replaced barrel up until no earlier than the late 1950s. It is obvious that yours has a factory-made 2" barrel, not a shortened barrel of greater length.