I would suggest a slightly different timeline and order of events than has been offered above.
Like your drum, the model 4160 snare initially had no knurling on the shell, a Microsensitive throw and round head screws to mount the lugs.
The knurling was introduced in about 1965/66.
The Microsensitive throw was replaced with the Lightning throw in about 1967.
The round head screws were replaced with hex heads in about 1967/68.
Therefore, your drum would be from prior to about 1965/66 based upon the lack of knurling. Without a paper label displaying a serial number, it is difficult to refine this estimate further.