Among other resources, try our US Government documents collection! A title to consider: Reference Documents on Disarmament Matter, US DOCS PR 34:11/3:D 1-42. It focuses on the late 1950s, and includes letters from then President Eisenhower, memos from Soviet negotiators and more.
Many of our government documents can be found in our catalog, and you are always welcome to ask about them at our reference desk. You are also welcome to contact our government documents librarian, Lori Lampert (email@example.com).