Using the menu bar with user entries: Removing entries

I would like for the user to be able to add her own entries to the menu bar for the main window, something like this:

And I'm considering different options for how to deal with removing items from the menu. So far these are the ideas that I have:

A remove menu item can be added for each menu entry (and the sets of two menu entries can be separated with a horizontal line for example)
A popup can be shown when clicking on the menu entry (rather than activating it), allowing the option to remove. Then the user would have to use the same popup for activating/triggering that menu entry (making things a little bit slower)
Right clicking (I'm not sure if this is supported on all platforms and I'm building a cross-platform application)

Or maybe it's just better to move this into a list inside a window in the application? (Or another option I haven't considered yet?)

Grateful for your help and with kind regards, Tord