Apple Safari browser 11.0.1

Open safari take cursor on top menu bar , click on History > show History .

Simultaneously open user library macOS Sierra: Library folder

Click on Caches folder select all contents ( use keys command and A ) delete them command and delete the caches column has zero contents , you can see in the screen shot just dragged both windows side by side , the browsing history is still there .

But a moment caches content will start to rebuild again and as these are temporarily files and will again create .

In your question you asked -

Is there a way to remove the history cache whilst the browser is open?

If I wanted to remove ALL browser cache and not just the History what needs to be deleted?

Answered for that was as above - browser caches are stored in user library - Caches folder so delete them but your history is still intact .

Now , a different question how to delete the history and store website data that is in the form of cookies .

Take cursor on top menu bar > History > hold option key - in the column you will see clear History and keep website data click on it a pop - up window appears .

Click on clear History , this will clear all of your browsed history but save the website data .

Go to Finder and select your user/home folder. With that Finder window as the front window, either select Finder/View/Show View options or go command - J. When the View options opens, check ’Show Library Folder’. That should make your user library folder visible in your user/home folder. Select Library/Caches/com.apple.Safari/Cache.db and move it to the trash.

Go to Finder and select your user/home folder. With that Finder window as the front window, either select Finder/View/Show View options or go command - J. When the View options opens, check ’Show Library Folder’. That should make your user library folder visible in your user/home folder. Select Library/Safari. I would delete the history.db, the contents of the Database folder, the contents of the Local Storage folder, and the Webpageicons.db. Then Caches/com.apple.Safari/Cache.db

That should remove most, if not all, history.

I don't know how to explain this very well, but once an application is open, all the data is loaded into the 'system' and the only way to clear that loaded data is to quit and reopen the application. When you reopen the application, the data that was loaded last time doesn't exist, so it can't be loaded.

Have you tried going to Safari/History/Clear History?

You have to quit and reopen Safari for the changes to take effect.

Does folder fsCachedData which is at location ~/Library/caches/com.apple.safari also need to be deleted?

I would delete that one also.