The small tote screw is usually called #12-20 whitworth. But it was whitworth before it became BSW. 12-20 isn’t party of the BSW series. I think you occasionally see it as 7/32” – 20 tpi.
I took mine out of my #7 and It threads correctly into a 1/4”-20 nut, but it is too loose a fit
I see several sites that sell them. The most reasonable seems to be Highland Woodworking in the USA.