There is no practical way to directly modify the contents of a pop-up menu.
As you've already noted, you can edit the content of the Short-Cut toolbar as well as the Radial,pop-up but those are the only opportunities that users have.
That being said, there actually is a way to indirectly remove the 'Make Unique' option from the pop-up menu but I'm not sure I should be posting this 'hack' on a public website (which the Siemens Community site is). I would prefer to exchange this sort of information privately via email.
John R. Baker, P.E. (ret) EX-Product 'Evangelist' Irvine, CA