If you're only using these headings in the navigation pane, you could edit the lower-level styles and change their outline level to Body text; I believe this will keep them from showing up. That's assuming all the headings have been styled: if not, you may need to set up a new style and apply it – ctrl + Y [repeat last action that Word considers repeatable] is a great time-saver there. Don't know whether there's any way of fine-tuning the navigation-pane content the way you can tune a ToC.

I entirely agree that implementing styles is worthwhile – tip: I have Normal defined as Courier, magenta so I can instantly see where content has not had a "real" style applied – and that tidying up a non-styled document can be a pain. Not so sure, after decades as a consultant in many environments, that you can say "corporate environment" to suggest "correctly formatted Word file" <vbg>