Two observations:

First: Al-Hakim narrated the hadith in his al-Mustadrak (2/441), with an additional wording (1):

“The Messenger of Allah, peace and blessings be upon him, recited: ‘And if a prompting from Satan should provoke you, then seek refuge in Allah from Satan, the accursed.’”

He declared it authentic, and al-Dhahabi concurred with him. Their assessment would be correct, were it not for the fact that al-Hakim’s shaykh, ʿAbd Allah ibn Muhammad ibn Shakir, alone narrated this addition, to the exclusion of all the others who transmitted it from al-Aʿmash; it is therefore anomalous.

Second: Ibn Abi ʿAsim narrated the hadith in al-Ahad wa al-Mathani (2351), inserting Zirr ibn Hubaysh between ʿAdi ibn Thabit and Sulayman ibn Surad.

I consider this to be nothing other than one of the errors of the shaykh of Ibn Abi ʿAsim’s shaykh, Mahdi ibn Jaʿfar, who narrated it from Abu Muʿawiyah, from al-Aʿmash, in this manner. He was “truthful, but prone to errors,” as al-Hafiz Ibn Hajar stated in al-Taqrib.

As for the hadith of Muʿadh:

It was narrated by Abu Dawud (4780), al-Tirmidhi (3448), al-Nasaʾi in ʿAmal al-Yawm wa al-Laylah (389 and 390), Ibn al-Sunni (454), Ibn Abi Shaybah (8/534 and 10/350), ʿAbd ibn Humayd in his Musnad (111—the selections from it), al-Tayalisi (570), and Ahmad (5/240), through several routes from ʿAbd al-Malik ibn ʿUmayr, from ʿAbd al-Rahman ibn Abi Layla, from Muʿadh, from the Prophet, peace and blessings be upon him, with similar wording.