It’s a little difficult to provide definitive advice without knowing how far in advance you’re making this decision, what size and type and how widely spread your entrants will be, how big the regatta is, or what the NOR, SIs, or other documents may say about the question, but if you’re talking about postponing individual days of racing, your photo does a pretty good job of showing what the Race Signals page of the RRS prescribes. If your competitors may be coming from shore in places where they won’t or can’t see the place where visual signals ashore are displayed, I hope you have written a way to reliably get the same information to those who won’t see it. 

If you’re talking about postponing the entire regatta, as a practical matter, you need to contact all who have entered to tell them, post an amendment to the NOR immediately to explain the new schedule, and spread the word quickly by as many ways as you can think of to prevent people from traveling to the event venue for no reason.

From the NOR Event perspective I don't think there are any rules. Except changing the schedule formally would require notice per whatever the stated time and place for notices to be posted but typically the morning of is still valid. The RC can abandon or postpone at any time for safety with the appropriate signals shown without modifying the SIs or NOR information.   I have postponed events a day before to save people from traveling and gotten flack for not at least trying to sail the day of.  I've also gotten flack for polling competitors during the skippers meeting the day of. But that's more personal grumbling than a case of any failure to follow the RRS on our part.