Hand Brake Grip

[Keep it stiff]

I need to tidy up a plastic grip. It had been painted previously but the paint was coming away, I cleaned it off with petrol however this revealed a rough finish which I want to tidy up. The grip is stuck fast on the shaft, it could be cut off but I would prefer to retain it and tidy it up. Any suggestions as to how? A product like this perhaps?

https://www.amazon.co.uk/PLASTIDIP-PLASTI-PLASTIC-...la-439483430585&psc=1