Why is Halahala Poison the one that came out of Churning of Ocean depicted in Blue in Shiva's throat? Any scripture backing to this?
Your inquiry is about the color of the KalaKuta poison and why it is depicted Blue in shivas throat?
The answer is the Kaalkuta poision which came out of Samudra manthan was not originally blue in color but because of it was the mala of the water it shown its effect on even Lord Shiva's throat. According to Mahabharata the nature of the poison was as that a fire attended with fumes.
अतिनिर्मथनादेव कालकूटस्तत : पर : |
जगदावृत्य सहसा सधूमोsग्निरिव ज्वलन ||41 ||
P. 60 But with the churning still going on, the poison Kalakuta appeared at last. Engulfing the Earth it suddenly blazed up like a fire attended with fumes.
The answer is provided in Shrimad Bhagvatam as follows.
तस्यापि दर्शयामास स्ववीर्यं जलकल्मष: ।
यच्चकार गले नीलं तच्च साधोर्विभूषणम् ॥ SB 8.7.43 ॥
tasyāpi darśayām āsa sva-vīryaṁ jala-kalmaṣaḥ
yac cakāra gale nīlaṁ tac ca sādhor vibhūṣaṇam
As if in defamation, the poison born from the Ocean of Milk manifested its potency by marking Lord Śiva’s neck with a bluish line. That line, however, is now accepted as an ornament of the Lord.
The blue color of Lord Shiva's throte became his ornament afterwards. So the poison was not of blue color but due to it's effect , Lord Shiva's throat became blue. So the throat is depicted as blue and not the poison.