Before they went Metric, Stanley used an obscure thread for their knob & tote
Screws. It approximates a #12-20, but the thread profile is NOT of the National
Standard (NS) form; it's a rounded profile made by rolling.
A #12-20 NS tap & die can be obtained from Victor Machinery. It's not a perfect
fit, but it's functional.
Reproduction parts for old Stanley tools can be obtained from the St. James Bay
Tool Co. of Arizona. They also sell the taps & dies, though I don't know what
the thread form is. ( I'm inclined to think they are likely the correct Stanley
form, as St. James Bay makes good stuff. )
Whose green Handyman #4 has proven to be a very good plane after some fettling.