I wouldn't trust paypal with such a large order, but a credit card can be checked - for example, whether the delivery address matches the card holder address. Also many cards these days are registered with 3d secure, and require a password for authorization. So for such a large order you would probably want to ensure this was included, because if the password passess, then the card issuer or card holder are liable for any fraud, not the merchant. Many payment gateways offer an optional fraud check on the card for a small fee.
Ideally, bank transfer would be the best option for you, but at the same time if the buyer is legit, they may not like losing the protection their credit card is giving them.
Is this an unusually large order for your client? If so, it has a much higher chance of being fraudulent. 'if it sounds too good to be true...'