I agree with Murray Missile, both on the useful rust-dissolving action of vinegar and on the harmless effect of steel wool.


Vinegar takes several hours to overnight to dissolve rust, with perhaps some periodic light scrubbing to dissolve heavier rust faster.


Steel wool gets a bad rap only because it picks up dirt, sand and chrome flakes, which will then act as abrasives that cause scratches.

Steel wool, if it's coarse enough combined with too much pressure applied can indent the very thin chrome surface because of the softer (copper and nickel) layers underneath.
But, using finer grades of steel wool, with moderate pressure on clean surfaces, it's harmless on chromed steel and even on anodized aluminum.
Beware though of flaking chrome bits or any dirt or sand caught on a steel wool scrubbing surface, as these can produce scratches.
Using steel wool with plenty of water, and turning the pad frequently, will improve the effectiveness and safety because the surface won't tend to load up with detritus.

Buying Oxalic Acid powder and mixing just a teaspoon per quart of water produces great results in 2-4 hours and is by far the cheapest way to go.
I bought mine from an online taxidermy supply outfit and it was very cheap in bulk.