What is the authenticity of the story of 'Amr ibn 'Abd al-Wud al-'Amiri and his challenging the Companions in the Battle of the Trench, and 'Ali's going forth to fight him?

The incident of Ali ibn Abi Talib killing Amr ibn Wadd in the Battle of the Trench is famous and well-known among historians and biographers. Al-Bayhaqi narrated it in "As-Sunan Al-Kubra" with a chain of transmission from Ibn Ishaq, and likewise Al-Hakim in "Al-Mustadrak" with a connected chain, which Adh-Dhahabi authenticated. Imam Al-Shafi'i, Ibn Taymiyyah, Ibn Al-Qayyim, and others have also mentioned it. Therefore, there is no harm in mentioning and narrating this story.