First of all, the Shire is explicitly stated in many places to have been protected by the Rangers; for example in the Prologue:
They forgot or ignored what little they had ever known of the Guardians, and of the labours of those that made possible the long peace of the Shire. They were, in fact, sheltered, but they had ceased to remember it.
And in the Council of Elrond:
If Gondor, Boromir, has been a stalwart tower, we have played another part. Many evil things there are that your strong walls and bright swords do not stay. You know little of the lands beyond your bounds. Peace and freedom, do you say? The North would have known them little but for us. Fear would have destroyed them. But when dark things come from the houseless hills, or creep from sunless woods, they fly from us. What roads would any dare to tread, what safety would there be in quiet lands, or in the homes of simple men at night, if the Dúnedain were asleep, or were all gone into the grave?
Secondly, the timelessness of both Rivendell and Lórien is referred to as a feature that the Hobbits are unfamiliar with, to the extent that they explicitly refer to it quite often.
For evidence, see Bilbo's words in Many Meetings:
Time doesn't seem to pass here: it just is. A remarkable place altogether.
And in the Ring Goes South:
'Oh, I don't know. I can't count days in Rivendell,' said Bilbo. 'But quite long, I should think.'
And from Lothlórien:
They followed him as he stepped lightly up the grass-clad slopes. Though he walked and breathed, and about him living leaves and flowers were stirred by the same cool wind as fanned his face, Frodo felt that he was in a timeless land that did not fade or change or fall into forgetfulness. When he had gone and passed again into the outer world, still Frodo the wanderer from the Shire would walk there, upon the grass among elanor and niphredil in fair Lothlórien.
And from The Great River:
'And perhaps that was the way of it,' said Frodo. 'In that land, maybe, we were in a time that has elsewhere long gone by. It was not, I think, until Silverlode bore us back to Anduin that we returned to the time that flows through mortal lands to the Great Sea. And I don't remember any moon, either new or old, in Caras Galadhon: only stars by night and sun by day.'
The fact that this sense of timelessness is discussed among the Hobbits as though it was something unfamiliar to them confirms that it's something that the Shire doesn't have.
Finally, and most specifically, Gandalf (in Many Meetings) refers to the power in the Shire as being different to that in Rivendell:
Indeed there is a power in Rivendell to withstand the might of Mordor, for a while: and elsewhere other powers still dwell. There is power, too, of another kind in the Shire.
- The protection of the Shire from the outside world is already adequately explained,
- The "timelessness" of both Rivendell and Lórien is something that the Hobbits are explicitly unfamiliar with,
- There is no evidence of a similar effect in the Shire,
- And so there is no evidence of or need for Narya to explain anything about the Shire.