Can't really answer your question except to say exercise caution. Natural stone should be cleaned using the appropriate cleaners as they are susceptible to staining. I once had a customer use vinegar to clean a marble floor and the result was not a good one. Be weary of what you read online for this type of product.
I would strongly suggest you visit a specialty floor covering/tile store and see what they have available and have this discussion with a local expert.
A steamer would work quite well as most people use to much water when mopping their stone floors. First remove the grit with a soft broom or vacuum, then use the steamer. Do not put any harsh cleaners in with it. If need be use a neutral pH stone cleaner.