Let's say if even after the destruction of the One Ring, Sauron could reshape. (Though this isn't possible). There's still another way Tolkien addresses to defeat Sauron that many people miss. In
Letter 200 Tolkien brings up that it takes so much "power" for Sauron to reshape time and time again, that eventually he wouldn't have enough to reshape (even if the Ring wasn't destroyed).
Quote:
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'But that of course did not destroy the spirit, nor dismiss it from the world to which it was bound until the end. After the battle with Gilgalad and Elendil, Sauron took a long while to re-build, longer than he had done after the Downfall of Numenor (I suppose because each building-up used up some of the inherent energy of the spirit, which might be called the 'will' or the effective link between the indestructible mind and being and the realization of its imagination).'
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As Tolkien calls it the "will" or "inherent spirit," each "build up" Sauron uses to reform takes up his "spirit." And eventually just killing him enough times he would not have enough "will" to reform.