Hey Kristine,
Thanks for reaching out. Unfortunately, at this time putting the categories in the top menu of the page would be the only way to achieve some sort of submenu like in your screenshot.
This has the flaws that you describe—namely that it shows up everywhere on your site, not just the calendar page—but there is no other option at this time.
If you are clever with custom code, or willing to hire a professional to write custom code for you, then of course just about anything is possible! 🙂 But in terms of out-of-the-box features or simple options-panel settings and the like, there is no way to pull off what you describe here.
Sorry to disappoint!
George