Stanley used some odd screw and thread sizes on their fasteners, and I have no idea if old Stanley "made in America" threaded parts would work with newer Stanley "made in England" tools.
With regard to planes, the threads are actually Whitworth threadform.
Stanley inherited their plane designs from Bailey. Leonard Bailey first patented planes in the 1850’s, so used a standard thread of the day. But this was before the Sellers thread was conceived, and long before it became standardised in the U.S. as “National” threadform.
Stanley continued to use those threads till the end of U.S. production. The British factory used the same threads, as it was no drama for them to use a Whitworth thread, although some of the sizes (I think 9/64 was used) were “non standard”, as were some of the thread pitches (I think there are some that are neither BSW or BSF).
Some later Stanley tools used threads from the American National “Numbered” series that are now obsolete (the larger ones that overlapped fractional sizes) but again, that was standard for the day.
Some tools produced by the British factory were revised to use metric dimensions in the 1990’s. Examples are the “Yankee” screwdrivers, where a “B” after the part number indicates it uses metric sized bits. Personally, I think this was a daft decision, as every Yankee screwdriver from an original North Brothers, to a late 80’s tool uses the same bits, but the newest don’t!
Don’t know much about Spokeshaves, but I suspect U.S. and British tools (with a question mark over the very newest) use the same threads.
Taps and dies for Stanley threads are available if needed. I’ve encountered a couple of tools where threads appeared to be different, but in reality just needed cleaning out!