He hasn’t asked for you to ship without payment, just that he wants it shipping to work? That’s what I do, nobody at home during the day so get everything shipped to work.
Nothing wrong with that, if it’s an address registered with PayPal or one entered as an alternate address when they make the payment. But if it’s not, you lose Paypal’s payment protection. You send the goods, they reverse the transaction, you’re humped. Don’t do it.
If you want to give him the benefit of the doubt, ask him when he’s going to be back and ship it out then.
(Incidentally, what halfwit gives a complete stranger their home address and then tells them they’re going on holiday?)