[Legate of Amon Lanc]

Originally Posted by Mansun

If the Nazgul were capable of reaching the Shire, it should be possible for Sauron to send a greater host, including the Mouth of Sauron & archers with great speed on horseback to attack key targets.

You mean during their hunt for the Ring? No way. The Ringwraith themselves had a big problem with crossing the river unseen; Sauron had to make assault on Osgiliath to enable them to pass to the other shore. In the Unfinished Tales we read:

Originally Posted by The Hunt for the Ring

The Lord of Morgul therefore led his companions over Anduin, unclad and unmounted, and invisible to eyes, and yet a terror to all living things that they passed near. It was, maybe, on the first day of July that they went forth. They passed slowly and in stealth, through Anórien, and over the Entwade, and so into the Wold, and rumour of darkness and a dread of men knew not what went before them. They reached the west-shores of Anduin a little north of Sarn Gebir, as they had trysted; and there received horses and raiment that were secretly ferried over the River.

It was important for them to cross the River unseen. The only possibility to cross Anduin was at Osgiliath or at the Undeeps, but a host was not capable across any of them unnoticed; and either way, there were miles of Rohan and the Gap of Isen to pass (there was no other way; passing through the Mountains would be unimaginable). And that meant confrontation with the Rohirrim and/or Saruman when noticed.
Also, it was speed what Sauron needed: both speed and secrecy. That was what only the Ringwraith could do.
And last and the most important: Sauron would not entrust the quest for the Ring to no one else but his most trustworthy servants; and maybe even Mouth of Sauron was not the one to be trusted in that matter - after all, he still had (or better maybe "was capable of having") free will. But even if Sauron sent him with the Ringwraith (not that he probably won't use Mouth's skills better at home; rallying armies, diplomacy talks with Southron kings and Easterling chieftains etc.), he probably won't allow him to bring along a squad of followers: Sauron won't entrust them with such a task.
It's all summed up here:

Originally Posted by The Hunt for the Ring

At length [Sauron] resolved that no others would serve him in this case but his mightiest servants, the Ringwraiths, who had no will but his own, being each utterly subservient to the ring that had enslaved him, which Sauron held.