I am not at all certain what you mean by "delete Cortana."
The Cortana process is, quite literally, the replacement for Windows Search under Windows 10 and if you take exceptional measures to delete it then you will have a number of "unusual results."
You also cannot perpetually reject updates to Windows 10, and that is true no matter what edition of Windows 10 (Home, Pro, S, Education, Enterprise) is being used. From Pro on up you can delay them for increasingly long periods but eventually they will be applied. We're now over 2 years into Windows as a Service and that update philosophy is not going away.
I have said the following on another thread but what you can do as far as turning Cortana features off or on is directly dependent on the Version and Build number of Windows 10 a machine is running. Earlier versions gave you greater control and if you turned off the Personal Digital Assistant features ("Get to Know Me" was off) and turned "Include Web Results" off what you essentially created was the old Windows Search. If one did this those choices have stayed through ever major feature update so far.
The above being said, if you waited too long or did "interesting workarounds" to try to neuter Cortana rather than using the built-in options, a number of those options have disappeared (e.g., "Include Web Results").
Winaero Tweaker from winaero.com still contains these controls, and a number of others, to allow you to manage the behavior of Cortana and to neuter her back to basic Windows Search in its Desktop and Taskbar control section. You can still choose to show either the search box or the search icon in its place in the native Windows 10 taskbar settings. I've used only the icon for ages, and trigger Cortana/Windows Search far more often by simply hitting the Windows Key and immediately beginning to type my search terms than by point-and-click on the icon. When it comes to searching strictly on file name, which I do far more often than any other type of search, I have long preferred the Everything Search from voidtools.com.