Granted that “there is no smith’s forge in this Shire that could change it at all. Not even the anvils and furnaces of the Dwarves could do that […] nor was there ever any dragon, not even Ancalagon the Black, who could have harmed the One Ring, the Ruling Ring, for that was made by Sauron himself.”
And let’s assume that the obvious eagle hack can’t be done, for some reason.
But what they could have done was to drop the Ring into molten steel, shape it into a solid sphere, and bid Frodo cast that into Mount Doom.
Just think of the advantages! First, it would be impossible to recognise. Second, it would likely be harder for the Nazgul and Sauron himself to detect at distance. Third, however tempted Frodo was to put on the ring, he would have been unable to. Fourth, it would likely have been easier for him to cast it into the Crack of Doom in this form.
See, that’s the problem with Tolkien. He was a fine scholar, no doubt, a surpassingly great creative mind, and an always-good-sometimes-brilliant author. But he just didn’t think like an engineer.