If you go to Hobby Lobby, they have a sandpaper packet that goes up to 12,000. It is usually hanging just to the left of the Pinewood display, but not a part of that display.
I have been to three different stores, and the sandpaper is about 5 feet to the left in anohter display. Packet is about 3" X 10".
Personally, I would go all the way with each grit of 1000 or better, i.e. take less than 5 seconds per each grit, especially the lower grits. 8000 and 12000 maybe 10 seconds.
Finish off with a leather thong and Brasso. That will really put a shine on the axle.
We have been doing this for six years on my grandson's cars. They have all taken first place all the way to the Council race for a lot of years (in Arizona)