Is that the "it" in the controversial sentence "it looked as if it had been designed specifically for Rand" refers to the "weapon", which is also mentioned in the previous sentence alongside the scabbard.

In my opinion, it means that the proportions of the sword, especially its length, perfectly fit Rand's tallness.

I believe that makes more sense than the idea that Hawkwing had a scabbard with a dragon on it, or that the scabbard could survive under water for so many years. Also in the other quotes by Rand, he only mentions that the "weapon" was found beneath the statue and that the "sword" felt old. And as we see in the sentence before the controversial sentence, Rand explicitly differs between the weapon and the scabbard, i.e. the scabbard isn't a part of the weapon/sword in Rand's view.

If one follows my interpretation nothing else suggests that the scabbard is old. Probably it was then recently made for the sword, since the weapon was supposed to be a gift for the DR.