The M14 did not get adopted until 1957 replacing the Garand as the main battle rifle at that time. I expect a few prototypes of the M14 existed in 1950-1953 but not widely used nor ever adopted as such. I don't think many, if any, of those prototypes got used in Korea. And certainly would not have been called the M14 at that time nor routine issue rifle at that time either.
Unless he was in Korea after the initial hostilities had ended and it was a DMZ duty assignment.
But if you want to find something similar then Springfield makes a decent Semi Auto copy. There are a couple other higher end ones too.
Or if it is a Garand or Carbine your after then try the CMP.