Welcome to the forum. You have actually described the gun pretty well by summarizing what you know. That gun is a .38 Military and Police, which was S&W's bread-and-butter gun through the decades, with several million of them produced from 1899 until their successor models today. There were many engineering and production changes through the years, of course, but the M&P line of revolvers is pretty much regarded as a unified production block by S&W collectors.
The serial number you cite indicates that the gun was shipped in 1954. The stocks do sound like replacements, and it is entirely possible that it was fitted with a lanyard when your father went to work in motors several years after he was first hired.
In 1957 that particular model became known as the Model 10. The preceding specimens in that particular engineering specification became known in shorthand as Pre-10s. Those guns were introduced in 1948, and they are primarily distinguished from their immediate predecessors in having what is called the "short action." After WWII S&W set about reengineering their revolvers to produce a shorter hammer fall and consequently a faster lock time. The prewar and wartime revolvers (and some postwar) are called "long action" guns. The various models of short-action K-frame revolvers were phased in between 1947 and 1949. The larger N-frame revolvers went to the short-action in 1950.
Feel free to post photos of your father's gun. There is an abiding interest here in LE sidearms and duty handguns.