Don't worry about the Not Shipped. (You can actually mark it as Shipped manually but that might lead to further problems.)
Then use Sell Similar to relist the original but change the title to your customer's name* and adjust the asking price and shipping.
Give him a deadline (48 hours?).
If he buys the "New" listing, ship.
If he doesn't, you can Revise to a new title and revise price and shipping and it will be available to anyone.
*Easy for him to find and unlikely to be found by anyone else.