You can't legally charge extra fees for shipping once the transaction is complete. Yes, you could do some private money exchange or something but IF eBay finds out it could be a costly mistake.
Your best bet is to play within the rules. Buyer selected a wrong shipping method, then the correct thing to do is to cancel the order with the reason - something wrong with buyer's address. You have their emails on the eBay system as proof of that - retain those emails. Then relist the item and the buyer can purchase it again and select the correct shipping options.
Do not do what the buyer wants and try some offsite, underhanded way of sending you the shipping funds. Play within the eBay rules and stay protected.
