Expired Announcements Showing Up in Site Search

Hi there.  I've spent the last few weeks migrating my company's SharePoint Intranet from 2010 to online.

Before going live, I need to address an issue we had with announcements in 2010 and see what is the recommended solution for the online version of SP.

Announcements have an expires field that is used in the view to filter the announcements where expires is greater than [today]. The problem is that old announcements that have been filtered have a way of showing up when someone does a search on the site.

Should I:

A. Create a workflow that deletes the announcement after the expires date is reached.

B. Exclude all announcement web parts from the site search.

I'm leaning towards A because it might be helpful to have current announcements returned in the site search. I'm just not sure how to setup a workflow as they were kind of buggy in 2010 and as such didn't get used. This I will research, of course. Can a single workflow fire for multiple announcement web parts? (There are 30 between the top site and sub sites).

Is there maybe a better way to handle this unique situation?