[Inziladun]

Hm. Interesting premise. I agree that Vilya and Nenya seem to be actively wielded by Elrond and Galadriel in the defence of their respective abodes. I don't think that was the case with the Shire, however, even if Narya had the potential to provide a similar protection.
Sauron likely had known of the existence of Hobbits before the time of his capture of Gollum, but I doubt he had much more knowledge than that they did exist. He had returned to his stronghold at Dol Guldur around the year 1050 of the Third Age, when the Hobbits still dwelt near the Anduin. He would have been mainly occupied with gathering his strength then, though, and I wouldn't think he would have been able to do much information gathering. At any rate, most of the Hobbits apparently left around 1150, according to the Tale of Years. Therefore it doesn't seem likely he would have had much useful knowledge to aid him in finding the Shire. That's what he hoped to use Gollum for. It's also notable that, as Gandalf told Frodo, until the time of the War of the Ring he seems to have thought Hobbits beneath his notice and of no importance.
As for Gandalf using Narya, my suspicion is that in order to use its power as a means to hide the Shire, Gandalf would have been obliged to reside there, as Elrond and Galadriel did in Rivendell and Lórien. And keep in mind that he didn't know Bilbo's ring was the One until he made the journey to Minas Tirith to read Isildur's Scroll in 3017. When he learned of the Ring's true nature, Gandalf asked the Rangers to guard the Shire. That, plus the general unobtrusiveness of its inhabitants, was the Shire's protection.