Rewind knobs have a normal, right-hand thread, so that they tighten as you are rewinding the film.
A lot of rewind knobs have the same or close enough thread that you can borrow one for repair or temporary rewinding/opening the back - for example, rewind knobs on many different Nikons have the same thread, so you can swap them, although the undersides won't fit on all bodies equally well.
Not sure if it's clear but the missing rewind knob shouldn't have had anything to do with the rewind button not fully depressing. Occasionally you may find a situation where the rewind button doesn't fully press and catch when you hit the end of the roll, I think because the wind lever is under tension. Jiggling the lever and/or pressing the button deeply usually solves this, as far as I can tell.