You don't.
If you did not include(and pay for ) the Best Offer option in your auction neither you nor your customer should have been working on one.
If you have no bids, end the auction now.
Relist immediately, changing the title to your customer's eBay ID and the price to whatever you agreed. At the same time change the listing to Fixed Price/Buy It Now / Good Til Cancelled. Let the customer know what you have done so he can complete the purchase.
Tah - daah!
Possible problems.
You will still have to pay for the closed auction. You will pay listing and selling fees on the new BIN listing.
Give the buyer a deadline to purchase. If he misses the deadline, Revise the listing once again, returning to the original title and possibly the original price. Put him on your Blocked Bidder List as a timewaster.
