I always use a version of that first stance shown above as a fence.
It appears casual or as if you're only mildly interested or bored. Or like you're mulling over what they're saying. You can support your chin, rub your face or talk with your hands (the top hand) like this. Which gets their eyes used to movement of that hand.
Look where the top hand is in relation to their face (if they're standing in front of you, no doubt with shenanigans on their mind) I love having my hand that close to a man's face when he doesn't realize it. I find it quite comforting.
If you have to use that hand you can shove against them as you step back (if you want distance) or step in with your forward foot to create more of a shove, strike etc. Or hook punch, grab whatever. You can work anything from there.
I used that stance throughout my career as a cop, a bouncer and as a city guy. Never once did it fail me. Sure got me out of a lot of jams.