To clean or not to clean? (and how to clean?!)

Hello,

I purchased 3 chairs at a yard and found out from their labels that they are knoll saarinen tulip chairs. I know that cleaning a piece of antique furniture can seriously diminish its value, so all I've done is gently washed the chairs with a moist soapy rag to get off all the dust and cobwebs.

Still, you can see that they're still quite dingy/dirty. When I bought them, there were what looked like drip marks from someone spraying a bleach cleaner (might be visible in the pic).

Since these lighter "drip marks" are already there, should I try to clean the chairs to match these lighter sections, or should I leave them alone?

Thanks again for any info!

-Tim