The Rhydymwyn Valley works, near Mold, which housed mustard gas shells in World War 2, had been earmarked.
Whitehall's Property Services Agency wanted assurances that the site could withstand flashes or blasts.
But the Welsh Office changed its mind about needing an emergency storage base for the nation's "few valuable items".
Fears of nuclear war with the Soviet Union had prompted government departments across the UK in the 1980s to plan for the worst, papers released by the national archives have revealed.
The scheme to protect art treasures was not originally due to include Wales but it appears a Welsh Office civil servant had asked Whitehall to reconsider.
The Property Services Agency - part of the Department of the Environment - proposed using two of the 10 chambers at Rhydymwyn in which they would construct buildings to house the art.
However, Welsh Office interest in the scheme appeared to cool, as shown by a letter to the Home Office by civil servant Tony Vinall in which he said the officers who made the original request had now gone.
"Present thought is that, although we do have a few valuable items, we are not really to be compared with the great national 'treasure houses' and it would make more sense for our local custodians to crate their most important possessions and put them in the most suitable sub-basement accommodation," he wrote.
Mrs Thatcher's ministers considered launching the controversial poll tax in Wales before England, according to other files just released.
The documents released by the National Archives also show Conservative government advisers feared a repeat of the 1984-85 miners' strike the following winter.
They also revealed Mrs Thatcher was warned by her Welsh Secretary that funding cuts would have "most damaging" political effects.
Plans to hide art treasures in underground tunnels in north Wales if a civil or nuclear emergency arose during the 1980s have emerged.