A word, gesture or expression for a confident "shrug"

You are right. The shrug displays lack of concern when concern is just what should be displayed. I agree with cruthers in his looking in the eye. Nothing else could get the understanding across in such a compact and assured way. A long, telling, direct look in the eye along with any kind of speech would do. That would say "I don't know what you mean 'wink wink" Message transmitted.

While this is not a "word, gesture or expression" it is an action that gets across the meaning the OP was asking for.

I think you might be looking for a “nothing-to-hide” gesture. It shares with the shrug an open palm attitude, but the shoulders don’t rise up:

_{Image source: Dreamstime: A young man shows his two bare hands showing nothing to hide}

“I honestly don’t know.”

That’s the gesture. I don’t think there’s a single word to describe it though. You can get some ideas for phrasing by searching ”hands” “nothing to hide” “gesture”.

Here’s one result:

Illustrative gestures. Everyone produces gestures spontaneously and unwittingly as they speak. We may seldom think of our gestures consciously, but in practice we use them with great efficiency and sophistication to cover a surprisingly wide range of communication.... These include: Open palms at an angle. Gestures with palms showing (tilted to a 45 degree angle) signal candor and openness. When being truthful or forthcoming, people tend to use open gestures, showing their palms and wrists and spreading hands and arms away from their bodies, as if saying: “See, I have nothing to hide.”
_{Source: amanet.org — When Leaders Talk with Their Hands}

For dialog, this might suggest something like:

John, palms outstretched, replied, “Honestly, I don’t know anymore.”

Palms upturned, John offered his alibi: “I swear I don’t know, officer; I was at a work function until 7 PM that night.”

I don't think that there is an expression specifically for shrugging. 'Shrugging' falls into words like run, speak, wave, jump, etc. You have to add separate words to give an action context.

For your first example: John shrugged with a smirk, "I swear I don't know officer, I was at a work function until 7pm that night."

For your second example: John sullenly shrugged, "I just don't know anymore."