Can we simply view “atheism” as a subset of “skepticism” and leave it at that? It can be viewed as a peculiar form of skepticism about very particular truth-claims. (I am, of course, not focusing on strong forms of atheism that assert truth claims about the “non-existence of God” — I don’t even know what that means. I have enough trouble with metaphysical God-claims to try to deal with proofs for non-existence.
I would say no, that atheism is not just a subset of skepticism.
The reason for that is that skepticism is in one respect a methodology and atheism can be arrived at by different methodologies than skepticism. Skepticism as a deliberate methodology rules out knowledge claims about certain kinds of things in principle—whether this means ruling out that which cannot be directly observed (in which case you get extreme Humean skepticism which even doubts necessary causation) or ruling out anything that cannot be verified scientifically (as many modern, scientistic skeptics do).
Atheism could be arrived at metaphysically. One could be open to the god hypothesis in principle (even if it is not, say, a scientific hypothesis) and simply think that the metaphysical evidence is wanting or that a non-theist explanation is superior to a theist one. In the latter case, the alternative hypotheses to theism might even equally speculative in kind as theism but just have better arguments in its favor.Those atheists exist, they are relevant and should not be definitionally excluded.
Alternatively, we may define skepticism more modestly as a hesitancy to affirm, rather than a flat out denial of all beliefs which do not meet some particular criterion. So the modest skeptic might say, “I do not say that there are no ghosts, only that I cannot affirm that there are ghosts or affirm that any known evidence implies that there likely are, but they still might exist.” Atheism may legitimately take the form of a resistance to affirm the existence of gods and be a default “lack of belief” atheism. But some of us are not merely skeptical and unwilling to affirm that there are gods but actually think we can affirm with reasonable enough confidence for a knowledge claim that there are no gods. Who is merely “skeptical” that there really is an Aquaman or a Zeus? No one I know. Everyone I know is damn near certain about it. Well, I am the same way about Yahweh and Jesus and Allah and all other personal gods. I see no difference between any of them and Aquaman and Zeus. I am not merely skeptical and unwilling to affirm belief in them. I affirm that they do not exist.