I’ve hear they went metic also, but I thought that was a fable. ( the modern Sweetheart planes are metric)

Another screw size Stanley and copy cat Record used is 3/16 -20 or 10 -20 Or 7/32 – 20 TPi whitworth ( I’ve seen all mentioned) the small screw on the larger plane totes for instance. Record may have switched.
If you have Stanley plane see if that fits.
But then you have to go to EBay or find a friend who has a metal lathe. Once or twice a year I go to a friends house and use his lathe to make screws and such.

I miraculously did find some Whitworth at a chain of stores called Fasteners Inc. But I think they stopped carrying it.

BSW doesn’t have a 24 TPI size. Their screws in that range are 26 TPI.

1/20” is about 1.27 mm pitch. I know 1.25 mm screws are made in 5 mm and 6 mm size, and again, for a couple turns that might work.
With machining slop such things are possible. I have an old Delta lunchbox planer I needed screws for, and figuring it was UNC I bought screws and they fit.
I later found out the planer was made in Taiwan and was all metric!
So some sizes can be a direct swap almost. You just have to try..

I fortunately have a local store that is very well stocked in Metric and UNC, I take tools to the store and just browse the bins to see what works.