On the basis of the buyer not cooperating, you might be able to contact eBay and have them appeal, or cover you for the refund. It's best to contact their eBay for business page on Twitter, Facebook, etc, and explain the situation. Ask them what your options are to not take the loss. I don't know what their policy is in this situation, but from time to time sellers do get lucky with courtesy refunds in scenarios where they aren't to blame.
If the buyer has not opened an actual return, and has only messaged you just leave it. Let them know that you are more than happy to assist them with the insurance process, but if they do not wish to participate in a claim you cannot offer a refund for carrier damages. In this scenario, as long as they do not open a return with eBay it's over with unless they change their mind and give the insurance the info. The return window will eventually close, and you did the right thing by helping to open an insurance claim. If the buyer refuses to cooperate, there is nothing you can do.
If after this they open a return, you have to contact eBay and explain the situation to see if eBay might be able to cover you due to the buyer refusing to participate in the insurance process. Unless you get really lucky and eBay nerfs the return, you will still have to respond to the return by any deadline and provide a return shipping label. After the item is returned, eBay might cover you in some way.
After that, the worst thing that can happen is the buyer can leave you a negative feedback. If they do that, eBay will likely remove it for you because you provided good customer service and the buyer did not act in good faith. If you receive a negative feedback that is in bad faith, go to this link, scroll down to 'email us', and then explain the situation: https://www.ebay.ca/help/selling/selling/seller-levels-performance-standards/appeal-defect?id=4871
For high volume sellers who do not sell expensive items, insurance at an extra cost is usually not worth it unless it is very cheap. Usually it is cheaper in the long run to pocket the insurance cost and cover any losses with "self-insurance". An example is that the US shipping service I use called Chit Chats offers insurance for a very low rate of 49 cents for the first $100. Let's say I send 700 packages a year to the US, self insurance (aka putting 49 cents into a jar instead of giving it to the carrier) nets me $343 per year. You can't pick and choose which packages are going to be lost or destroyed. So if my average sale price is $30, I have to refund 12 or more packages a year before self insurance doesn't make sense. Odds are, out of 700 packages, 1 or 2 might be lost or damaged not 12.
Now do that formula with a different shipping service that charges a few dollars for insurance, and it will quickly become apparent that insurance doesn't make much sense for high volume sellers.
Insurance is more useful for casual or low volume sellers, especially those that are selling more expensive items. If refunding an order out of pocket would be a huge ordeal, I would gamble on insurance, even if the customer complying is not guaranteed.
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