Here's food for thought,

You might want to try the product called NeveRdull. It comes in a tin with cotton batting. You should be able to use this and not worry too much about removing what zinc may be on the spokes. It's an ultra-light abrasive.

You rub it on, work a little more on the tarnished areas then let it dry. Knock off the dried residue with a clean shop towel. Repeat if necessary. Then use something like WD to protect it.