The CNG site gives the weight for the 1/192 stater but not the diameter. (It also says it may just be an underweight 1/96 stater.) Being electrum it probably has a lower density than the gold fanam which might account for the light weight. (I have also seen fanams as small as 4.5 mm)
Read closer, it actually says that the coin in the Kayhan collection is more likely an underweight 1/96 stater. There's no diameter because its from a printed sale, and the coins in the catalog are of course to scale. It actually measures about 3mm.
But it also seems to imply that the coin in the sale and the coin in the Kayhan collection are the same variety and the second one known. Anyway you gave me the size information, 3 mm so yes it is smaller than the smallest fanam I know of. So yes this looks to be the smallest circulating coin.
The smallest coin I have is a 1950 10 cent from the Netherlands, with Queen Juliana on the face. Measures 14mm in diameter.
Yes, I have some of those too. Around the turn of the millennium, before it was taken out of circulation, that 10 cent coin (dubbeltje) was the world's smallest circulating coin as far as I know. Officially the diameter is 15 mm. The coin was so small because it used to be a silver piece - but even when they were Cu-Ni (1948-2001), the size remained the same ... Christian