wd 40s an oil Alex
It wont work.

If you use anything too rough it'll scratch then you'll have hours of work polishing the scratch out if its possible at all.
Maybe if all else fails look for a toothpaste with 'small crystals' like Colgate whitening!
The more you polish the less shiny it'll be.
Watch the wavey patten -> Sharpe edge.The Hamon. It can change or rub off/change pattern if you Over Do It.
Gently small circles lightly- then stop oil it, Check it then try again if not good enough.
If you go too quickly it could heat up the sword and discolour the blade will look like you put it in the fire....not good.