Then you will want to have a look at the Clear History extension for Firefox.

Or if you prefer you could have modified the Privacy Options ahead of time.

Even selecting Never remember history may not be the best choice for you.

Clear Browsing History in Firefox with a Keyboard Shortcut

What you need is a quick and easy on-demand option.

After

After restarting you will find a new menu entry in your History Menu.

Links

Download the Clear History extension (Mozilla Add-ons)

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