I know that Vishnu Sahasranamam was told by Pitamaha Bhishma to Yudhishthira ORALLY. However who was the writer and who had made the hard copy of the same to do chanting of this mantra and when?
As you have already stated in the question, Bhishma told Vishnu Sahasranama to Pandavas. To be more precise, it was Yudhushtira who asked for it. The names present in the stotra are the most famous names of Lord Vishnu which were already sung by great men and rishis.
yāni nāmāni gauṇāni vikhyātāni mahātmanaḥ|
ṛṣibhiḥ parigītāni tāni vakṣyāmi bhūtayē ||
I am giving for the benefit of all, those names of His which are far-famed, which are indicative of His attributes, and which find a place in the exalted hymns of the ṛṣis.
To answer your question who composed those names into a hard copy, it is the same one who wrote the Mahabharata i.e Veda Vyasa because these are part of the Mahabharata itself. This is made clear in the Anga nyaasa of the stotra (installing deity in our body). Every mantra has a rishi (seer), chandas (metre), deity.
Asya śrī viṣṇu-sahasranāma-stotra mahā mantrasya
śrī vedavyāso bhagavān ṛṣiḥ
For this great sacred chant "Thousand names of Vishnu", Sri Veda Vyasa is the divine rishi.
So, the answer is Veda Vyasa.