The fabric is quite durable. So, I would try a prespray that has both enzymes, solvency and detergents (potentially an amoniated one)+ a detergent rinse.
Wipe well with towels and leave enough time to check for wicking and correct if necessary.
Test one chair as Richard suggests, if practical (most times it will require an extra trip which for me makes it impractical). Price according to amount of chairs being cleaned and actual time spent.
Some here use encapsulating products. I'm not a big fan on upholstery (don't consider it cleaning), though if price is an issue, it may do. If so, nuke them.
Explain in advance that the crunchy sound the chairs will make afterwards, is the sound of cleanliness
