(1) Copy the CSS of the Secondary Menu and replace the current Header Menu style. This seemed tedious and then I would also lose the Header Menu style.
(2) Set the Secondary Menu to my main menu and my Header Menu to nothing. Unfortunately, setting the Header Menu to nothing makes a default menu appear. So now I had 2 menu instead of just my Main menu.
The Trick: I created a new custom menu named it Blank Menu and did not add any menu items. I assigned the Blank Menu to the Header Menu and my Main menu to the Secondary Menu position. Now since there were no menu items in the Blank Menu, the Header Menu CSS had nothing to be applied to so the Header Menu didn’t appear.
I was left with just my Main menu using the Secondary Header style.