At the council Elrond is against sending the Ring to the shores as that is the way that Sauron expects and the roads will be strongly guarded.
Do we get any indication that it was de facto so? Why didn't Sauron destroy the Grey Havens and the White Towers?
As far as we know, Sauron did not guard the Western Road. I don't think we see any evidence of guards or spies along it. Of course, there might have been some, that we did not hear about. Elrond's scouts, however, don't seem to have found any (if they even scouted the Western Road?)
Of course, there was an attack on Bree by 'bad men full o' thievery and mischief', early in the New Year that resulted in five dead from the Breeland. If these were under direction from anyone, it was more likely Saruman than Sauron. Had the Ring set out from Rivendell as late as 25 December, the Company might have run into this trouble. However, any sizable Company should have been able to deal with the 'set-to' in Bree with the help of the Breelanders.
Saruman's ruffians (actually perhaps more Lotho's ruffians at this point, but with some connection to Saruman) also seem to have appeared in the Shire around the turn of the year. So, again, if the Ring had not left Rivendell until 25 December, the Company might have run into some trouble there.
So, there seem to have been agents of Saruman (in fairly small numbers) on the Western Road by New Year. I don't think that Saruman and Sauron were exactly cooperating as allies, so if Sauron had any spies along the road, I guess they were few and unobtrusive. Otherwise conflict between Saruman's and Sauron's agents might have ensued.
Elrond is dead set against the Western Road. "The westward road seems easiest. Therefore it must be shunned. It will be watched. Too often the Elves have fled that way." But, there is little evidence that Sauron actually had spies, and certainly did not have forces along that route.
If the Ring had left Rivendell earlier (say mid-November), then they probably would have passed through the Shire before Saruman's thugs arrived (especially if mounted).
The Western Road, I think, would have been a good route for the Company. West to the Havens, then take ship towards the mouth of the Anduin. The Ring could enter Mordor via passes near the headwaters of the Poros River. The ship could continue on to Minas Tirith with Boromir and Aragorn. Due to ships being speedier than walking, and due to them sailing both day and night, the actual travel time for this route would be about the same as the route taken, despite the distance covered being considerably further.
If Sauron had detected this route, it might have caused him lots of wild conjectures as to what was the planned destination of the Ring.
One danger might have been the possible despatch of a fleet from Umbar to try to intercept the Elvish ship. However, I would guess that Elvish ships might well be able to sail rings around the Corsairs?