Looks like a pre number K-38 Target Masterpiece, should have SN marked on the the cylinder, under the barrel on the flat, on the frame, and inside the stocks. Nice S&W.
Yeah, pre model 15. The hammer says it's a 4 or 5 screw. A pic of the other side would be a bit more telling.
Pre model number 17, the 15 is the K-38 Combat Masterpiece with the 4” barrel.
I think you're right that Smith called the 4" K-frame .38 Special revolver with adjustable sights the Combat Masterpiece. It later became the Model 15.
I think the 6" version of that gun was called the K-38 Target Masterpiece, and became the Model 14. It was a target revolver, and it had two cousins: the K-22 in .22 LR, which became the M-17, and the K-32 in .32 Smith & Wesson, which became the Model 16.
But anything is possible with S&W.
Okie John