ML, the revolver in your pictures shows a pre Mod 12 K frame Airweight, not a pre Mod 37 J frame Airweight. The K frame is much larger than the J frame. However, it is true that pre Mod 36 and Mod 37s do not have a C prefix serial number and that pre Mod K frames did.
I think these pictures are from a current Gunbroker auction in which the seller either mis-typed the data or just doesn't know the difference. I noticed this ad on Gunbroker a few weeks ago when I did a search using the word Airweight.
Another big clue is that the pictured gun has a 6 shot cylinder which denotes a K frame and a J frame has a 5 shot cylinder. There are other differences including the shape of the hammer, and that K frames used a leaf spring and J frames use a coiled spring. The spring I am referring to is contained in the grip frame so it's not visible in the pictures.
HTH