You can create a time off type in the system to be hidden. This means that it will not be shown on ANY calendars and not shown to the employee in Self service.
You can create a time off type by going to
Admin > HR > Time off Management > Time off types
Under display setting you will see Hidden type as an option
Please be sure to yes this to yes before submitting
Please Note : As a default once the Hidden type is set to YES the Bookable and Public Calendar will set to NO. This is something that cannot be changed
You can choose how to set the Out of Office field to determine how this shows on the Out of office marker on Employee card and (optionally) in the Directory.