Your Putnam is "post 1866" when Putnam moved into their "new shops" and transitioned production to the heavier legs. A quick look at your tailstock would put this after 1870 or so when detailing became more uniform. If you give us better (larger) pix (use the uploader and try to pick/size your pix above 1000 square) of more details we might be able to date it closer.
The box wrenches are hard. These are very easily left behind in a box and most who buy the lathe are slow to pick up on "associated ephemera" connected with a lathe ownership transfer.
Your best bet may be to "simulate" one by starting with a 6 point hex socket, carefully grinding the outside of the socket into a hex, welding on a handle which you'll have to "hand forge" to approximate shape and size. Or, do as Putnam did and make one from scratch. They're a little crude and inconsistent - which IMHO is part of the charm.
I have the wrench which I can make pix/measurements as required. But I also have the Putnam lathe - and (sorry) this wrench is not for you - yet.
There is a respondent here on the board who may contact you. He has a wrench - I believe. And may be willing to sell it to you as he is parting out his 14" Putnam which is incomplete in other appointments.
As to the male square wrench for the chuck, these exist in multitude on Ebay and can be usually bought for less than the price of a dinner at Olive Garden. They're all about the same pretty much up to the present day.
OBTW, your chuck is not consistent with the age of your lathe. Male screws protruding from the diameter of the chuck ("knuckle busters" as they're affectionately known) would have been time appropriate for this lathe. Followed (possibly) by a similar chuck with the male square screws "sunk" inside the diameter. Followed by a chuck with female square screws which is yours. Your chuck from say 1885 onwards.
Joe in NH
Who has both a Putnam tailstock wrench, and a Shepard, Lathe & Co. wrench which are both virtually identical - and probably made by the same source.