72 Schwinn Varsity axle nut?

[redditor]

I'm pretty new to refurbishing bikes, and I just purchased a 72 Schwinn Varsity from a yard sale. It was not in very good condition, so I'm trying to fix it up. I noticed that a nut from the front wheel axle is missing. I've taken the bike to a local bike repair shop that had been suggested to me, and I've visited the local Ace Hardware. Neither had a fitting nut, as the (apparently) 5/16" axle's threading isn't standard. (Note: the wheel is a Schwinn Tubular S-6 for a 27X1 1/4 tire, and mounted on the front if that matters.)

I've read that there's a lot that isn't standard about the older Schwinns and I've hunted around the internet for a place that sells a nut that'll fit the threading, but I haven't really found anything. I can't find the specifications of the nut, and no sellers have enough information for me to assume any given nut is right.

So I was wondering, does anyone know what I need and/or where to purchase it? I'm hoping it's a nut that I could find in a hardware store, but that seems a bit unlikely.