Howdy
It does appear to be a Model 10-1. (Model 10, dash 1). The 4" heavy barrel was introduced in 1959 with the Model 10-1. However, if it is a -1 it should say so on the frame under the yoke. If it just says Mod 10, it is a Model 10, no dash. The first version of the gun. According to SCSW the Model 10 was introduced in 1957, -1 with the heavy barrel in 1959. -2 and -3 with the extractor rod thread changed to left hand came along in 1961.
According to SCSW the SN range for 1961 - 1962 is C 474149 - C 622699, which would put C 452xxx towards the beginning of that period.
But anybody who has studied S&W for a while knows there are always exceptions to every rule.
I must take exception to anybody who thinks a revolver from the early 1960s is old. Heck, I'm older than that.
The grips are called Magna grips. Magna grips extend up and cover a side plate screw at the corner of the frame. Various versions of them were made as early as 1936, up until around 1967. With the uncheckered diamond around the screw, they are called Diamond Center Magnas.
See if you can carefully remove the grips, without damaging the screw. Look on the underside. S&W usually marked the SN on the underside of one of the grips before they left the factory. Sometimes in pencil, sometimes stamped in. If the SN on the grips matches the SN under the butt, the gun left the factory with those grips.