He used a 2" M&P in in the TV series. If you saw a flat latch, it must have been an M&P Airweight. There's a pretty good photo here, but it doesn't show the latch:
http://www.imfdb.org/w/images/d/d4/Dragn67_5.jpg
The serial number doesn't jive. C175806 is too early for an M&P Airweight, it wasn't produced yet. It would date to around 1950 and would have a half moon front sight. There's a ramp front sight in the photo. D175806 would date to 1969-1970 which is too late for a flat latch. Neither of those series went over 1,000,000 so it couldn't have been 1755806.