The only useful action he can take is to start an Item Not Received dispute with eBay/Paypal.
Don't panic. Lawsuit threats are completely smoke and mirrors. Only the eBay Dispute should concern you.
You would get a message from eBay notifying you of the Dispute. If you used a tracked/Delivery Confirmed shipping service, give the number in the Dispute. If checking the Canada Post website gives you a delivery date, add that too. This information will either end the dispute in your favour, or give the parcel more days to arrive.
I'm assuming your customer is American. They get angry real easy. It would take at least 10 and possibly 20 days for your item to hit his doorstep.
If you did not buy tracking, make the refund and write it off as a business expense and learning opportunity. As a coin dealer, you will get a lot of these claims if you are using LetterPost/Light Packet. It 's the demographic you are selling into. This will end the transaction and you will not have any black marks on your selling account.
If you do not refund, and cannot prove delivery, PP will refund the buyer and take the money from your PP account. Plus you get a black mark.
Since most of your sales seem to be under $30, perhaps the best bet in future is to use Light Packet and self-insurance. Light Packet because you can give an invoice number to the customer that will reassure an honest buyer that the parcel is on its way, and will discourage a scammer who thinks the number indicates that the parcel is tracked.
Self insurance means only that you add a small amount to every shipping fee as insurance against the occasional claim.
Don't worry. At worst if you refund him you are out the cost of shipping, some eBay fees, and your procurement cost .
Just don't get into an arguement. Right or wrong, you will not win.
