This.
Okay, so if I get no response, do I ship it to the Paypal address?
Contact an eBay representative. They will strongly recommend you not ship to the other address. Also, because you have talked to them and told them the situation, they will have a record of what you've told them (and it is also recorded in the eBay messaging system). That way, if you ship to the correct address and the buyer leaves you negative feedback, you can contact eBay and they'll have evidence on your side that you potentially can use to have the negative feedback removed.
Wait for the buyer to respond. Tell the buyer you follow eBay policies, for your own protection. Be polite and courteous, of course. The buyer should understand and be willing to work with you, including honoring your preference for following eBay policies.
The buyer is completely at fault here. The buyer should have asked you BEFORE HITTING THE BIN if you'd be willing to ship to another address. You would have said "no," and the buyer wouldn't have hit the BIN, and there'd be no problem. It was presumptuous on the buyer's part to assume you would violate eBay policy.