I have 4" blue 1950 Model 38/44 Heavy Duty serial S 94944. It is not lettered but I believe it shipped possibly early 1953. Looking at the SWCA database, we find another Heavy Duty, S 95054, 4" nickel, shipped 6/24/53.
Note added 12/17: I searched the ship date requests and found no requests for 1950 Model .44 Target ship dates. However, I found requests for HD ship dates and combined them with the SWCA database finding:
.38/44 HD serial S93563 November 1952.
.38/44 HD serial S95054 June 1953.
.38/44 HD serial S95700 August 1953.
One could assume that the majority of HD's in the S94xxx range shipped Dec 1952 - June 1953. I'll go further by speculating that my HD S94944 shipped in May or June 1953. Because HD's were primarily LE service firearms that moved quickly through inventory this speculation may not hold for IWK2HT's 1950 .44 Target # S94002, which was probably ordered by a distributor or retailer. Nevertheless I guestimate his .44 Target shipped in the first quarter of 1953. It just depends on how long this particular gun sat in inventory.
Note added 12/22/17: Roy Jinks reports that my .38/44 Heavy Duty S94944 shipped May, 1953.