You should only ship to the confirmed Paypal address.
It should be part of your terms of your listing, to reinforce eBay's policies and guidelines.
If the item is over $250 including shipping, you need to get adult signature required on delivery.
If the customer persists, you will have to explain the only way to do this if for you to refund the money, and for them to resend it with Paypal with the desired address that they want it shipped to as their address given with their payment.
When the payment is received, you can check your Paypal to see if it's eligible for seller protection.
I would only advise shipping something it you are eligible for seller protection, and don't forget about the adult signature if needed.
The only way I would do an exception is maybe for a previous customer, but even then it would put YOU at risk, not the customer.