What happens when you right-click into the Window of any text processing app is determined by the app. No way to intercept, modify or extend this on a standard user/programmer level. It might be possible using some kind of kernel level injection, but that's way out of my scope.

What you can do is using a session level hotkey. So, you need an invisible background app which registers this hotkey and when the hotkey is typed your invisible background app may show a popup menu at the current position of the cursor and offer functions which may interact with the clipboard. I have a private tool for my own purposes (named zClipMan) which exactly uses this approach, so I can safely confirm it's technically possible.

Nevertheless, I doubt it is possible using PowerShell. Showing such popup menu virtually out of nothing is not rocket science but requires some coding on Win32 API level which isn't easily in scope for PowerShell. My own tool is written in C++.