Do i need to send out change the dates? Or just change the date in the invitation?

Like so many others we have to push our wedding back, but only by 3 months. Save the dates already went out and i wanted to sent invitations out end of September/october bc the wedding is semi destination for 95% of the guests.

Do i have to send change the date cards? Or can i just send invitations around October with the updated date. We also have a wedding website we already updated. Could i just post to FB/email everyone? I let the people who would be flying in know personally.

I just feel like it's an unnecessary expense and we're dealing with the cost being doubled already since we're going form off to high season.