I'm really not sure that Dead Horse Trope fits here.
Mainly because I'm no convinced the trope of playing this straight exists or has ever existed. I think possibly there's been a confusion between a trope that's so dead, parodying it has become a trope and a trope that was just meant to be ironic in the first place.
Looking at the examples, the only examples that aren't using the whistle ironically are ones making fun of a characters stupidity. IE the trope being parodied is the supposed parody of the dead horse trope.
I think as far as tropes go as tools for writers, the not-so-innocent whistle is used and has always been used to imply that a character is guilty of an act and is very weakly feigning innocence and far from a subversion,lampshade hanging, or parody, this is how the trope is played straight.
I think that this page has enough examples to be organized into categories. Is there an index for tropes in that state?
In between Not Even Human and Not Quite Human