Why isn't there a setting where it simply won't keep the history?
This seems to work for me:
Open the Browser
Select the Windows icon. This will display any open browser windows.
Select the minus symbol (-) next to any open window listed. This seems to clear the previous page history.
Easiest way I found to do this is with an app called History Eraser, The icon looks like one of the old school erasers with the red cardboard around it. From what I can see it cleans everything all at once.