Walkerwek just did a post explaining the process a couple of days ago , cant remember which post it was on off the top of my head . I think it was about a scratched watch bezel !
From memory you will need to strip the buckle from the strap so you can use wet and dry on it. I have also read Scothbrite will work. You need a stick like missus emery boards. You can buy these they are called Buff Sticks , but I think a lolly stick with wet and dry paper wrapped or emery board is the same thing and cheaper/ less hassle !
You will need different grades wet and dry or Scotchbrite start low grade example 800 and finish/ smooth with high grade example 1200 . If it was me I would get a load of different grades Halfords sell multipacks or local Car accessory places sell buy the sheet, then try say 1000 grit ,do half a dozen rubs then look . Whats it look like ,to deep to shallow then go up or down a grade for half a dozen rubs , check again . I would say that you need to clamp the work steady in a vice, so you can concentrate on full sweeps to get the brushed effect right to the edges. I would only go forward ( one way )with the paper/stick and not rub back and forth , this Im pretty confident will give you a terrible finish ! If you think in terms of how they do it at the factory on a polisher with a wheel or belt spinning one way only.
Can you not get a used one from Ebay to save any dramas !