If you don't offer a refund now, you will have to weigh your hope in the buyer's patience against the likelihood of getting a defect if the buyer escalates the INR, because without tracking you will definitely lose the case. If you've just started selling, the last thing you want is a defect and/or negative FB.
Even if the buyer says he'll be patient and wait, he may change his mind when it comes to leaving feedback, and answer "No" when asked if the parcel arrived by such-and-such a date. Whether you get a late defect at that point will depend on what eBay's delivery estimate is -- it should be shown under the "Shipping" tab on your listing, although eBay isn't always very forthcoming or accurate when displaying their own delivery estimates. Or the buyer may get nervous and decide to escalate the case after all. In which event, you'll be forced to refund anyway in order to avoid a defect.
If this is an item of relatively high value and I were a new seller, I think I'd send a message to the buyer asking that they wait one more week, making it clear that I'd refund immediately thereafter if the item didn't arrive. Provide an actual refund date, don't be vague. See how the buyer responds. If they agree, be prepared to refund, then ask the buyer if they would kindly let you re-invoice them if the item does eventually arrive. Of course, without tracking, you'll have to rely on the buyer's honesty to inform you if the item arrives.
If it's an item of fairly low value, weigh that value against the value to your business of avoiding a defect and potential negative FB at your stage of selling. If you have a high turnover, you may be able to absorb the loss and the defect without much impact. If you have a low sales rate, even one defect is a serious matter.
The unfortunate lesson to be learned here is -- never send anything by ground. EBay just isn't tolerant of long delivery times anymore, and if you keep using ground services, and get defects as a result, you'll find that eBay will downgrade your seller status to the point where you're practically invisible to buyers.
Lastly, shipping overseas has become a terrible dilemma for smaller sellers on eBay. Should you use tracking to protect yourself against late shipment defects (and thus turn off a whole lot of buyers from paying the exorbitant shipping costs)? Or should you use non-tracked air parcel (Small Packet Air) and extend your displayed handling/shipping time on the listing to help shield yourself from late shipment issues? And by "late shipment issues", I mean as perceived by eBay and buyers, not as determined by Canada Post. Of course, if you're selling large-sized or heavy items, you have an additional problem, since Small Packet Air has size and weight restrictions. Then you're into high-priced tracked services anyway.
By the way, was this parcel insured? If so, and if you need to refund, you may be able to pursue recompense from Canada Post (or whoever your insurer was).
I hope this turns out well for you, but honestly, don't use ground shipping if you want to keep selling successfully on eBay.
