The BSW threads are a British Standard Pipe Thread, Whitworth form, which implies a "straight thread." I'm not sure what the Brits do, but in the US nearly all actual plumbing uses a tapered thread for easier sealing on "common pipe threads," and if that's the case BSW tools in that specific size are probably somewhat "special."
The UNS is an "originally US" standard, and is approved for international use by most other (esp NATO) nations, but the "S" on the end indicates a "special" configuration that may be a little harder to find tooling for.
A 1/4 x 20 UNC (1/4-20UNC) probably would be very close to the 1/4 x 20 BSW, and is very much a common standard in the US; but the "misfit" might be questionable due to the frequent use of "soft metals" (and plastics?) for sound equipment hardware. The "flank angle" on the threads would be expected to be about 5 degrees different, which might or might not be a problem depending on the "precision level" of the parts you need to mount.
As you seem to have the problem parts well in hand, this is superfluous information, so I didn't check the finer points.