Consider the Firefox Privacy Browser. It uses the Safari rendering/processing engine, but shells it with in "Anonymous" mode, which should mean it never saves any history at all, provided you close it (really kill close, not just background).
Create a Shortcut and call it "Clean Up" (or something else of your choice) - then you can use Siri to take you to the menu where you can clear browser data. It's not completely automatic - but it makes it easier. Just say "Hey Siri, Clean Up"
Open the Shortcuts app, create a shortcut - select Open URLs and add this path: prefs:root=SAFARI&path=CLEAR_HISTORY_AND_DATA