Being asked to charge a customer's credit card with extra and pass it on to a shipper? #ItsAScam
Credit card details are regularly phished, stolen from hacked websites or obtained in other ways. If scammers try to buy something with the card then they will have to deal with getting the item delivered, so it is much easier to get an unsuspecting merchant to charge the card for them and send them some money.
If a customer wants to use a particular shipper (or other service provider) and needs you to charge extra to his credit card and forward the extra money to the shipper then it's always a scam. If a customer wants to use a particular shipper and it is not one that you have a relationship with, then let them make the arrangements and pay for it directly.
Variations on this scam include booking/ordering and then having to cancel and requesting a refund by Western Union, Moneygram or bank transfer or possibly ordering high value items and having them shipped overseas.
Never agree to charge the customer's card for more than the cost of the items/services that you are providing
Always process refunds back onto the card that you charged them from
Beware of customers who provide a different card, rather than resolving a simple problem with the one they gave you.