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If the item arrived damaged file a insurance claim with USPS or whatever shipper you used, provided the class of postage you used has insurance. It's a painful process and will probably require the assistance of your buyer. Have them keep the item and the original packing since USPS will probably want them to take it into a local PO for inspection. If the postal worker, usually the postmaster, agrees that the item was damaged in shipping they will keep it and file the electronic forms to start the refund process. It can take up to 90 days for you to get a check from USPS. I have had two of these in the last few years and USPS paid in both cases. Not sure how you shipped the item but the timetable for filing claims with USPS is below.
One buyer had opened a claim damaged in shipping but as soon as I asked them to keep the item and original packing that I was filing a claim with USPS and they would probably be contacted by USPS to bring the item into the post office for inspection they dropped/closed the claim.
NAD cases are another matter and you may as well refund. If you don't and the buyer asks eBay to step in you will loose and eBay will unilaterally take the funds from your account and you will probably not get the item back. As others noted no returns does not mean no refunds.
