We need to change an upcoming Board meeting date, due to a conflicting event. I THINK we need to present the revised Board meeting schedule to the Board as an action item for approval, and then change the date on our website. Am I correct?

Yes, the change in date should be done by board action, as the original meeting schedule was (I assume) approved by board action.  Once the change is approved, it can then be updated on your website. For more information on this question, Ask Betsy's Team.