What internet site did you find your information on? The suggestion made previously to obtain a S&W letter is your best bet if it is important enough to know the shipping date.
It really has nothing to do with authentication, and all about when it was actually shipped and where.
For $50 Smith & Wesson will provide a very nicely done letter worthy of display for your revolver with the date of manufacture.
Mine is in the 946xx range and if I remember correctly was manufactured in 1943.
I believe the letter to ad $50 in value to the piece.