Is there an externality if someone buys all stock of some merchandise? On one hand, if they buy all of everything and there's still demand then they've taken it away from other people. On the other hand, it kind of feels like that should be accounted for in the supply curve, and it's not an externality so much as the producers not having known the correct supply curve?
From the Oxford dictionary: (emphasis added by me)
A consequence of an industrial or commercial activity which affects other parties without this being reflected in market prices...
Another way to put this is that externalities are not the results of market rivalry. So if you and I are bidding on the same item on e-Bay, and you are buying it, I kind of suffer, but this is within the market context, this is not abnormal. Whereas if you buy a new stereo system on e-Bay and then keep me up all night by listening to loud music, this happens outside of the market context (unless I sold you the right to listen to loud music) and is an externality.
In case of a Cournot-oligopolies one firm's increased production would also harm other firms by lowering the price. But this is not an externality either, as it is the result of normal market rivalry for the consumers.
It seems like in the situation you are describing you are not facing an externality, as it everything happens in a market context. Perhaps there is information asymmetry, as the store was understocked. (This would require additional assumptions and is not the only possible explanation.)
You can try drawing up an Edgeworth box for a two-person, two-good economy to see this more clearly. It should be easy to show that overall utility is maximized for equilibria near the center of the diagram, where the two agents share both goods equally.
Since you're talking about externalities, this implies that you're looking at maximizing social welfare. You can certainly construct heterogenous preferences such that one agent hoarding 100% of a good is optimal, but they are probably not that realistic.