I'd take the card out and repacck it.
First remove the card, place it in an antistatic bag, wrap it in bubble wrap and put the whole thing in a plastic bag, then secure with tape. Put the card/bag/bubble wrap into the PC case and tape it to the top/bottom or a side panel as seems best to secure it for transit.
Remember: the customer ahs to remove and install the card, try not to mummyfy it with tape:)
The insurance will depend, all I can suggest is that you read the contract carefully and work with the customer if they return the goods.
Yes, I'd have to say that that sounds like the best option. Thank you, sir! Now the only question is where can I find an anti-static bag?