Your question can be answered from tafsir ibn Kathir who refuted this and said it is among the so called israeeliyat unfortunately qtafsir didn't mention this IMO important part of the text and jumped forward quoting a long hadith :( while explaining the meaning of (2:36)
... And We said, "Go down, [all of you], as enemies to one another, and you will have upon the earth a place of settlement and provision for a time."
This is the sentence from tafsir ibn Kathir:
وقد ذكر المفسرون من السلف كالسدي بأسانيده ، وأبي العالية ، ووهب بن منبه وغيرهم هاهنا أخبارا إسرائيلية عن قصة الحية ، وإبليس ، وكيف جرى من دخول إبليس إلى الجنة ووسوسته ، وسنبسط ذلك إن شاء الله ، في سورة الأعراف ، فهناك القصة أبسط منها هاهنا ، والله الموفق .
--- ( My own Translation take it carefully) ---
And some of the muffasiroon like as-Suddi (with his sanads/narrator chains), Abu al-'Aaliyah, Wahb ibn Munabbih and others have quoted here some israeliyyat of the story of the serpent, and Iblis, and how Iblis entered the Janah and whispered and we will quote this later insha' Allah in surat al-A'raaf as there the story is longer than here. My Allah give success.
Imam al-Qurtobi in his tafsir said:
ولا خلاف بين أهل التأويل وغيرهم أن إبليس كان متولي إغواء آدم ، واختلف في الكيفية ، فقال ابن مسعود وابن عباس وجمهور العلماء أغواهما مشافهة ، ودليل ذلك قوله تعالى : وقاسمهما إني لكما لمن الناصحين والمقاسمة ظاهرها المشافهة
--- (My own translation take it with care) ---
There's no dispute about the fact that Iblees has taken the "duty" or "burden" to tamper Adam, but they differed on how this was achieved, ibn Mas'ud and ibn 'Abbas and the majority of scholars said it was orally based on 7:21 as swearing means speaking one to one.
... وقال بعضهم ، وذكره عبد الرزاق عن وهب بن منبه : دخل الجنة في فم الحية
While some said, this was quoted by Abdurrzaq from Wahb ibn Munabbih: He entered the Jannah in the mouth of a serpent ...
As Wahb ibn Minabbih was well versed in Jewish tradition, the origin of the stories telling that Iblees disguised himself in or as a serpent seem to have their origin in non-Muslim sources. As there's no authentic hadith of the Messenger of Allah () quoting this!
One narration of as-Sudi -i found- is quoted in the tafsir (narration #8289) of ibn abi Hatem ابن أبي حاتم:
عَنِ السُّدِّيِّ ، عَمَّنْ حَدَّثَهُ ، عَنِ ابْنِ عَبَّاسٍ ، قَالَ : " فَآتَاهُمَا إِبْلِيسُ فَقَالَ : ( مَا نَهَاكُمَا رَبُّكُمَا عَنْ هَذِهِ الشَّجَرَةِ ) ، فَلَمْ يُصَدِّقَاهُ حَتَّى دَخَلَ فِي جَوْفِ الْحَيَّةِ فَكَلَّمَهُمَا "
--- (My own translation take it carefully) ---
... from as-Sudi, from the person who told him, from ibn 'Abbas, who said: "Then Iblees came to them and said: "Your Lord did not forbid you this tree ..." but they didn't believe him until he entered (hid himself) inside the serpent and spoke to them
Also read in this fatwa English and this one in Arabic (only), which concludes with the statement that such stories shouldn't be taken seriously as they have their origin in traditions of people of the book and the hadith quoted by as-Sudi from ibn 'Abbas is not authentic as the narrator whom got this statement from ibn Abbas is unknown