I would leave a comment .. but I'm incognito .. uh, maybe not
The suggested shortcut target
"C:\Program Files (x86)\Opera\launcher.exe" --private
will not launch Opera in private mode unless Opera is already running (so I have to open my shortcut twice)
Is there a better solution?
It does launch Opera in private mode for me the moment I opened it.
From my knowledge, we can access different Opera shortcuts to launch Opera. So if you edited the shortcut target via the start menu, it may not launch in private mode. Perhaps you can try launching Opera first, right click the Opera icon in the taskbar, right-click on Opera to edit properties and edit the shortcut target. I hope it will work for you.