Do you have a hardware store nearby? Go find the machine screw section and find the nuts. Look at the ones between No. 3 and No .10 and just try screwing it into each nut until you find the size that fits. Probably the easiest thing to do since you'll most likely have to go to the same hardware store to get a replacement anyway. Some stores even have a little piece of wood with different size nuts/bolts on there at one spot so you can find the right one there.
I'm guessing it's probably a 4-56 or a 5-56 but it's impossible to tell from the picture. Can you tell if the thread pitch is the same (just put the two shafts against each other, if they are the threads will align). Do you have a pair of calipers or a 1/100ths scale to measure the diameter of the threads? If so refer to this... http://www.csgnetwork.com/screwinfo.html
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