No way in H*ll would I be handing over my credit card information to these sorts of establishments. Justifying turning over this sort of personal information to scam outfits by saying "well I can get a chargeback" seems to be a pointless rationale. I wouldn't even admit to having a credit card on me!
If you must participate in buying art, going to teahouses, etc. at places shown to you by strangers who almost 100% have a different agenda, then negotiate a price upfront, get it in writing, have your service or buy your product, pay cash, get a receipt for the payment, and take any product with you rather than depend on shipping.
If the amount is too large for petty cash, you likely don't know what you're doing and have no business doing a transaction in these types of establishments in the first place. You have been warned.