You can create a time off type in Natural HR which can be hidden by going to

Administration > HR > Time off management > Time off types 

In the 'Display settings' section, you will see 'Hidden type' as an option. Please be sure to set this to 'Yes' before submitting.

Hidden time off types do not get displayed on ANY calendars and are not available to employees via Self service - they are still visible to administrators, HR and managers for their teams. Hidden time off types tend to be used for balance adjustments which do not need to be visible to the employee.

Any time off type set to 'Hidden type' 'Yes' will set 'Viewable on public calendar' to 'No', and 'Bookable by employees' also to 'No' regardless of what settings you choose for these options.

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.