In the pushbutton callback you can add this code to populate the popup menu through its 'String' property:
set(handles.YourPopupMenu,'String',[cellstr(get(handles.popupmenu_XYRegistration_Z,'String')') {'YourNewValue'}]);
So basically you get the current strings in the popup menu as a cell array of strings and then you concatenate vertically (using []), adding 'YourNewValue' at the end.