nail varnish is easy to come by (easier for some than others 😉 ) and can be pretty hard and is low viscosity to good for filling very fine scratches. Yours don’t look like fine scratches!
You could try nail varnish though, should be able to pick up some black and not get any strange looks at this time of year!
you could also use red first and then black so you can see if the black is wearing down and redo your repair when needed. Get some very fine wet and dry – at least P1200 but I would get P2500. Wrap it round a wooden dowel for accurate work on the scratch area and then do a final polish in the way cartoon characters dry their backsides with towels (sorry, only way I can think to describe it)
PS no idea what the base material is in nail varnish (off to google it), but it could be a polyacrylate so pretty tough.