Prevent ComboBox from showing the currently selected item

I’m trying to use a combobox as a “File…” menu in my plugin. I want the name that is displayed on the header button to be “File” and I don’t want that to change when a menu selection is made. As far as I can tell, the only way to achieve this with ComboBox is to “unselect” any item that gets selected right after a selection gets made, but this results in a weird graphical glitch where for a second we see the selection that got made instead of the menu name at the top.