Anyone who knows better feel free to correct me, but to the best of my knowledge S&W never used a flat-latch style thumbpiece on any K-Frame revolver except for the Military & Police Airweight which would become the Model 12 in 1957.
So, what you have is a 1952-1954 M&P Airweight based on the fact the M&P Airweight was introduced in 1952, and the change to the standard thumbpiece occurred in 1966. The hammer is the earlier style with the rounded spur and fine checkering. The hammer style changed to the modern nearly flat spur with coarse checkering in 1953-1954 as I recall.
The difference in color between the barrel and the frame which is distinctly black also indicate this is an M&P Airweight. The cylinder in the photo is somewhat uncertain and may even be the early Aluminum type. There seems to be no difference in color between the frame and cylinder, and the wear on the leading edge of the cylinder appears distinctly white compared to the color of the remainder of the cylinder. Since a prop gun would, at best, only be shooting blanks this wouldn't be an issue for film use.
The supposed serial number mentioned elsewhere as coming from the "Dragnet" episode "The Shooting Board", is spurious. The earliest M&P Airweight had a serial number of C223999. All M&P Airweights will have either a "C" or "D" serial number.