A 6 lug Chrome snare without the center knurling and "6T" as a model number is likely a model 4106T - with the "T" indicating that there is a tone control (muffler) installed. The serial number of 96539 would typically indicate a drum from the 1967-68 time frame.
Most of the 4106 model drums that I have seen in chrome were made earlier in the decade. There are several drums in my log from the serial number range of your drum and later that carried the 4106 model number that were brushed aluminum finish. (See the 1971 catalog - http://www.gretschdrums.com/ebooks/1971/index.html#/37/). There are a few reported as chrome and one that had a gold tone brushed aluminum. It appears that Gretsch applied the 4106 model number to 6 lug snares with several different finishes. Could you provide a picture or two of the drum so that I can take a look? Also, what do the screws which mount the lug casings look like? Are they hexagonal head or rounded slotted screws?
Note that any estimate I make is based upon the theory that Gretsch used serial numbers in a particular somewhat systematic way. I describe this in my published guide and have decribed the methodology in detail in prior posts here and on another drum forum. It is just my opinion based upon review of several thousand drums. Not everyone agrees with the theory, so be mindful of that. Regardless of its age, what you have is a Gretsch drum that you like.
Rick