Is there a term for words that have a single meaning or are only used in a single context?

It's a "stormy petrel." The idea, as described on the linked page, is that (for example) you never (or, at least, rarely) find a petrel that's not stormy. Similarly, "all shrift is short," and lots of other examples. One of the ones there is in fact "every skirl is of bagpipes."

Closely related are fossil words, which have no meaning outside of a certain set phrase. "Bated" survives only in "bated breath", for example.

There are several terms for closely related concepts:

• A nonce word is a word that somebody made up for a localized purpose. Apart from fossilized words, those nonce words that caught on are probably the major part of this group.

• A cranberry morpheme is a morpheme that has no meaning on its own, and exists only as part of one or a small number of words. (It's named after the "cran" of "cranberry".) A fossil word is similarly a word that is used only in a small number of phrases (but whose state is specifically due to the original meaning's obsolescence).

• A hapax legomenon (of a particular corpus) is a word that appears exactly once.

There is no clear word or term that conveys words that have a single meaning or are only used in a single context. The nearest match is the word unequivocal:

having only one possible meaning or interpretation.