You shouldn't, at least not completely. The giants in the book are giants--very large humanoids. They are not mountains that transform into something else.

Tolkien never actually describes them, so we don't know if they're stone-giants because they live among the stones of the mountains, because they throw stones, or because they are made of stone. I actually pictured them as Pdonis describes them, as very large humanoids, although I can't be sure.

But I don't think we can definitively settle the question of the giants' form, as we simply don't have enough data. So I suggest we branch out to another unanswerable question: would Gandalf have used Emacs or Vim? How about Sauron?

Tolkien doesn't come right out and say "giants are very large humanoids", but so what? They are described as throwing stones, which clearly implies that they are humanoids. The "very large" part is implied by the word "giant"; also, of course, there are plenty of mythological references to giants, in particular in Norse mythology, which Tolkien is known to have drawn upon, and they're always very large humanoids.