409 will be slightly magnetic, 304 or any 300 series is NOT magnetic at all.
If you use steel wool, you will be embedding steel particles into the surface; it WILL rust, however small the spots.
What is done in fabrication shops is to color code the grinding/sanding wheels. If you have new, unused sanding/grinding wheels or sheets, it does not matter what alloy they are used on; carbon steel, stainless steel, aluminum, titanium, hastelloy, etc., once they have been used on a particular alloy, they have that alloy embedded into them for the same reason that you cannot get all the sawdust off of sandpaper that you have used.
Use new sandpaper of whatever grit you choose. The fastest way to polish is to start with a coarser grit and work your way to finer. Personally, I would hire it done or purchase already polished tips, they are not that expensive.
Certified Welding Inspector.