Since the buyer opened a case you will get an item not received mark in you INR metrics but a few of those will not affect you. Whatever you do will not change that.
If you use ebay shipping and send with tracking, you will get a late mark as the tracking will show that you did not send the item within your handling time or that it arrived before the estimated delivery date. When you don't use tracking the only way to get a late mark is if the buyer checks off in feedback that the item was late so sending it without tracking wouldn't affect your late shipment metrics.
The best thing to do imo is to refund the buyer through the case that they opened. If you send a new item ebay isn't going to know that you did and may end up refunding the buyer anyway. That would result in an unresolved case defect being given to you which isn't a good thing.
If you are willing to sell to the buyer again, they can repurchase the item after they are refunded. Or, you can refund them and still send them another one at no cost to them. I would only do that if I was confident that they are being honest about having not received the item. If you think they are being dishonest (most people are honest imo) then you should put them on your blocked bidder list.
