I've been wondering about that, too. The "here is a hand" argument shows a couple places at least, "A Defense of Common Sense" and "Proof of an External World." In the first he is arguing against universal or global skepticism and the hands argument is part of it, but in the second I think the "hands" argument is more directed at showing that one can know common sense intuitions like the existence of an external, material world. Still, he seems quite certain skepticism is false (not just about about external, material objects but global skepticism).
Here's a quote from "External World" (SEP):
I knew that there was one hand in the place indicated by combining a certain gesture with my first utterance of ‘here’ and that there was another in the different place indicated by combining a certain gesture with my second utterance of ‘here’. How absurd it would be to suggest that I did not know it, but only believed it, and that perhaps it was not the case! You might as well suggest that I do not know that I am now standing up and talking — that perhaps after all I'm not, and that it's not quite certain that I am! (‘Proof of an External World’ 166)
Here's an interesting detail. According to the SEP entry, he distinguishes between proving an external world and proving one can know there is an external world.
I have sometimes distinguished between two different propositions, each of which has been made by some philosophers, namely (1) the proposition ‘there are no material things’ and (2) the proposition ‘Nobody knows for certain that there are any material things’. And in my latest British Academy lecture called ‘Proof of an External World’ … I implied with regard to the first of these propositions that it could be proved to be false in such a way as this; namely, by holding up one of your hands and saying ‘This hand is a material thing; therefore there is at least one material thing’. But with regard to the second of the two propositions …. I do not think I have ever implied that it could be proved to be false in any such simple way … (‘A Reply to my Critics’ 668)
For the life of me, I can't make sense of that distinction. I don't see how one can show there is an external world without also showing, by entailment, that at least one person knows there is an external world.
ETA: I should add, the author of the SEP article doesn't think Moore is arguing against skepticism, per se, but against the rejection of an empirical truism, i.e., I have hands. I'm not sure that helps Moore's argument all that much. From the SEP author:
Although, as I have indicated, Moore did not intend his ‘proof’ as a refutation of skepticism, he did frequently argue against skeptical views; and in his early writings, despite the passage quoted just now, he does sometimes give the impression that he thinks one can refute skepticism by simply bringing forward a straightforward case of knowledge, such as ‘I know that this is a pencil’. But on examination it turns out that his strategy here is more subtle; he wants to argue that we get our understanding of knowledge primarily through straightforward cases of this kind, and thus that skeptical arguments are self-undermining: for, on the one hand, they rely on general principles about the limits of knowledge and thus assume some understanding of knowledge but, on the other hand, they undermine this understanding by implying that there are no such straightforward cases of it.