Learn English – An idiom for “a hidden clue that will unravel a thestery”

Practicing strategic incompetence

This often involves intentionally doing things poorly or incorrectly so as to have unwanted responsibility taken away, but a more subtle form is to plan for so long that failure comes as a natural outcome.

For example, if you really don't want to have the responsibility for planning office parties, you could start talking about your plans for decorating with orange and yellow teddy bears, serving anchovy pizza with no sauce (one large per person, right?), and entertaining with live organ or polka music. Plus everyone will have to dress as a person from history and also go by the name of an animal (Aardvark and Lemur, please come help me carry these 172 pizzas!).

"By the stars" would not necessarily suggest that the speaker has no idea. It sounds more similar to "By Jov" or "Oh my God" which can suggest a pretty wide array of reactions, from surprise and bewilderment to outrage. Also, using it the way you want to can even come across as a type of truism, since the general meaning of the sentence it will be used in is that the speaker has no clue, so there is no need to use it both as an opening line and then reiterate it several words later.

"By the stars" is a nice choice of idiom to express the speaker's surprise, so you can keep using it, as long as you agree to let go of the intended meaning of "I don't have the faintest idea". It just makes the sentence it's used in sound needlessly convoluted and there's a very good chance that your readers will not understand it the same way you intended it.