Today the IQuickNavigatorItemProvider interface holds the overridable methods for SortOrder and Dictionary GetMenuItems. There is however no way to retrieve the current default shipment by Episerver for the quick navigator menu.
In the CMS edition it would then be plausible with an extended method to get the default items and as developer either remove them or adjust them (e.g. text, url, etc.). The GetMenuItems doesn't really give you the current items as it is for now.
Would be sweet to handle this entirely! :)
The IQuickNavigatorItemProvider you create will just be added next to the other providers as you're only supposed to add more items instead of modifying the existing menus. The idea is that it's not only one QuickNavigatorItemProvider.
However if you want to find the existing providers you should be able to use
If you want to remove all and implement your own (I don't really recommend this) you can see how I eject all implementations in https://github.com/alfnilsson/episerverutils/blob/master/EpiserverFindUI/DependencyResolverInitialization.cs
In that example I'm also reusing the original implementations in my new implementation.