Child-murderer or child murderer?

During an episode of Archer, he criticized a journalist’s grammar for her misuse of the word ‘child-murderer’. She meant one who murders children, and Archer argued in using the hyphenated form, she implied the accused man is a child who murders. Is this correct?

I searched “child-murder” and “child-murderer”, only to find columns eschewing the hyphen in nearly all cases. Instead, the columnists, relied on context as to whether they are referring to a child who murders or one who murders children. I, however, am purely interested in the proper use of the hyphen in this situation, as it could possibly extend to other situations as well. The trouble seems to arise from child not having an adjective or descriptive form. With ‘teen’, one does not run into this problem:

• Teenage murderer vs teen murderer

However, if one uses ‘adolescent murderer’, it becomes unclear as to whether one means an adolescent who murders or… you get the picture. This problem arises from adolescent being both an adjective and noun; a hyphen can resolve the ambiguity. But once again, how should the hyphen be used?

I found a similar question: What is the plural of 'only child'?

I err on the side of only-children, in the event that ‘only children’ reads as ‘just/simply/merely children’. Some suggested entirely new phrasing, while others say that the context is sufficient. I don’t believe one should change his entire sentence when proper use of the hyphen can get his meaning across just fine, and even when context is suitable, proper grammar is still rule of law.