I had the same thing. I didn't have the "Cortana & Search" setting even though results showed up using a Cortana search. The classic settings were not there anymore and the new settings under windows settings were not there either. I didn't see a way to "turn it on" so to speak. So thats' when I thought perhaps through a group policy something wasn't active.
I think the reason I was able to get the cortana icon to appear in the Windows Setting is because I was able to go into the group policy editor and check into the "Search Setting" and "Allow Cortana", it was "Not Configured" (which makes sense on why I was getting a cortana search but not a way to control it, it wasn't disabled just not configured). So, I changed it to "Enabled". Restarted, and then the cortana icon appeared in the Windows Setting and I was able to fully control it from there.
I have the 65 bit pro version of windows 10 that has the group policy editor, I don't think the home edition has it? I think there lies your dilemma? If it doesn't have it, I thought the settings could be accomplished thru the registry. Hope this information helps provide further insight. Thanks.
Edited by sjf99, 05 November 2017 - 01:35 PM.