However, when this is done within WebView, it pops up WebView's own context menu.
As of version 2.2, there is a method called
setContextMenuEnabled that allows me to disable it. But when I do so, nothing pops up at all.
How can I get this to work correctly?
Create your own plugin that handles right clicks and shows a small popup menu. Have alook in the sopurce code of the
contextmenu plugin shipped with tinymce. You may use most of it's code for this and only need to implement the menu points yourself.