You would expect .05 (or .047) but that's not always the case. I had a Custom Shop Precision that came with an .022, and an American Vintage that came with a .100, both were bought new so I know they were original.
The tone knob certainly worked on my CS Precision, the .022 should give an even broader range so your problem may be something else. Still, nothing wrong with trying an .05.
Not really such thing as a guitar capacitor. What works, works. Gibson used some very small value capacitors on its old basses.