There is no way to prevent user seeing folder names from the mail, if you give access to your calendar.
The mail in the folder will not be seen, but the folder names can, and their names only is confidential for management.
These folder are not private because some secretaries ...
Once upon a time alphaWorks at IBM had created a proof-of-concept product called NotesBuddy. It allowed you to access your Notes mail without loading the Notes client. ***It could even READ YOUR MAIL AND SAMETIME CHATS TO YOU***
It was only 6MB in size, worked with your personal POP mail ...