Is there a term for "*cough*<something>*cough*"?

The best I can come up with is the idiom to say something under your breath.

Closely related words which may cover this are to mutter, mumble or mussitate.

Although I haven't focus grouped it, "cough" as a verb of saying sounds OK to me and expresses the desired meaning. As in

"I crashed your truck," the porter coughed.

or

She coughed the words "thirty seconds," in response to her mother's demand to know how long she had spent considering her options.

It's a parenthetical comment, demarcated with a pair of "ahem," rather than the usual parenthesis (as this comment is), or by commas, as this one is, marking the parenthetical comment.

The use of "cough" as opposed to "ahem" seems to be fairly modern, but ahem is an onomatopoeia (a word that replicates or nearly replicates a sound that it represents) for throat clearing.

Similar parenthetical onmatopoeia include "sigh," "whimper," "moan," "groan," and "ah." Frank Herbert used "Ahhmmm" for the character of Count Hasimir Fenring in his dune novels, occasionally as parenthetical markers.

This can be called a hem, and is often written as ahem.

I'm not sure this covers the case where the speaker actually coughs over a word.