Its just a basic stud and nut.
Looking at TM10-1562 (May 1943)
First image shows the carrier and associated parts.
Second page is just to show its held on by a simple nut.
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The nuts to actually hold the tire to the carrier look exactly like the inner tire lug, but with no outer threads. So if your grind/lathe off the threads of a standard inner lug nut, you'll have the same thing used on the spare tire carrier.
Early trucks did use a lock and key that would fit over the stud, but later models stopped this and went with a pin through a hold in the stud. Not sure if the nut changed to a castle nut. But photos show a chain and pin.
If you use the online parts manual seach and look for 2139480 you'll see the later items that include the pin