Hair's-breath refers to a very small distance or amount, and there are several synonyms that can be used in its place. One such word is "whisker," which is often used when referring to a narrow escape or a close call. Another synonym is "narrow margin," which is used to describe a situation where something almost didn't happen, but ended up doing so by the smallest possible degree. "Paper-thin" is also a synonym for hair's-breath and is often used to describe the narrowest of margins or distances. "Barely perceptible" is another synonym that can be used to describe something that is almost impossible to see or measure, but is still there nonetheless.
