You can hide/disable the built-in Navigation Buttons of the RadCalendar by property settings or CSS. See the Navigation Controls Settings documentation page for insights on this.
Also, the above documentation page provides details on the Month/Date Picker Popup which can be enabled when user clicks on the Title Area of the Title Bar, and this can be used to fast navigate to a specific month.
Alternatively, you can disable navigation buttons by setting the RadCalendar "EnableNavigation="false" and then implement external, associated RadButtons. You can handle calender navigation using JavaScript, setting the RadCalendar to postback and reset the month view.
Here's a somewhat similar application for you to use as a starting point: