Pic is helpful, thanks. What I would do there is resin cast a new one. It's simple and really rewarding. Make a latex mold of the knob, after smoothing out any wear on it first with a tiny bit of body filler or similar, then cast a new one (or ten) using resin and black powder, or use another colour if you like.
Silicone for the mold
Resin for the part
Pigments for the colour
I realise that you cannot pop in to those suppliers like I can, but I'm sure you could find similar products elsewhere...boat builders use most of the above products for example.
This is a pic of a badge I made for my Bristol....I only had one, they are not available, so I cold cast this with resin and 50% metal powders, then polished it up. It is indistinguishable from the original one.