If you take the chairs off site, you will need to check:
Liability insurance for working off site.
Van insurance for carrying goods.
Goods in transit insurance.
Do you need a carriers license these days for carrying other peoples property/goods? Such a long time since I did it.
Whats wrong with, as others have suggested, cleaning on-site? Use a waterproof drop sheet with an absorbent top sheet. You could use a classroom, the Hall even a corridor.
With these type of "conference" chairs, I'm in the same ballpark as AJB. My prices start from £2 per fabric panel, so £2 for the seat, £2 for the back, £2 for the reverse back, then there's fabric arms at extra depending on size, typically from 50p to £3 each. Smaller volumes like yours would be at a higher rate.
Safe and happy cleaning

The Ken