I have seen laundry detergent cause fish eyes, I always use disposable rags.

Contamination is always a concern, especially with a playfield. There is no telling what has been sprayed or wiped on over the years. All automotive paint manufacturers recommend the first step as wiping with wax and grease remover before you do anything else and disposable towels. Sanding over contamination can just grind it into the surface. Problems still occur, and frequently you never know why.

I think the eye dropper idea is your best bet, as long as it's pretty fresh it should be ok.
Here's what we use for a wiping cloth.

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