Is it significant that the birthmark is in the shape of a hand?

It is significant that Georgiana's birthmark is in the shape of a hand. In the very first paragraph of the story, the narrator says,

The higher intellect, the imagination, the spirit, and even the heart might all find their congenial aliment in pursuits which, as some of their ardent votaries believed, would ascend from one step of powerful intelligence to another, until the philosopher should lay his hand [my emphasis] the secret of creative force and perhaps make new worlds for himself. We know not whether Aylmer possessed this degree of faith in man's ultimate control over Nature.

In other words, then, the narrator describes some individuals who believe that humankind can aspire to create, just as one might conceive of God or Nature as creating. These people think that, with enough intellect, imagination, and passion, a man can "lay his hand"—claim for his own—the ability to create "new worlds." The narrator says that we do not know if Aylmer feels this way, but the events of the story make it seem as though he does.
Later, Aylmer tells Georgiana that she "came so nearly perfect from the hand of Nature" that her birthmark "shocks [him], as being the visible mark of earthly imperfection." In light of these quotations, then, the shape of Georgiana's birthmark seems to symbolize her "Natural" origins. She was created naturally, and as a result she has an imperfection. In fact, she must have have some imperfection because she is earthly, she is human—she is not divine (and thus, perfect). In attempting to lay his hands on the secrets of Nature, so to speak, Aylmer overreaches: when he renders Georgiana perfect by removing her birthmark, she cannot survive because nothing produced naturally can be perfect.