I have been getting rust on my chrome wires because they have a groove where water sits unless you dry them off after each shower (west Ireland!). I know you can use wire wool safely BUT it will leave tiny fragments of steel which instantly rust and stain. I just used Brass pot scourer for getting surface rust off very effectively. I even used it on all the chrome to clean off paint spots etc. They are liable to loose bits but are very cheap. Still need to find a tool to get behind the spokes as my fingers are a little too big. A small bottle brush does most of it but not that groove inside the spokes where you need a bit of pressure to clean it well.
Interesting. Pictures show something similar to steel wool but made of brass. Does it also come in grits or grades ?
I don’t know about grades but these do the job of removing that blueish corrosion on the chromed brass eg. front grill and of course rust spots etc.
I got them on Amazon -Kleeneze KL072177EU Euro 3.49 for 3.
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In South Africa they’re called ‘Goldy Locks’ pot scourers. 
You can also get Bronze Wool from marine stores.
Some use shoe laces, going from spoke to spoke
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