Two things to mention here:
first yes there is no possible way to remove the default search engines in the shortcut menu... on the UI.
Still there's a json-file in %opera-install-dir%/%your-opera-version%/resources named defaultpartnercontent.json.
Find your location (e.g. "de" for germany) and remove the search engines from there. Than the key is free for use again.
Also I'm pretty sure it was possible earlier and the reason opera removed it because of security reasons is pretty strange. What security reasons should that be?
Thank you so much! I've searching all day to resolve this 'local domain' issue and finally found a way, thanks to you!