Do we have a specific verb to express the action of the woman in the picture above?
I can list some phrases:
-Hold out your hand to say no
-put up your hand to say no
-put out your hand to say no
-straighten your arm to say no etc
When someone puts up their hand, it suggests that their hand is up in the air like someone who wants to ask or answer a question. I'd suggest
Collins: If you stick out part of your body, you extend it away from your body
The same expression could also be used for a hand shake. Perhaps the clearest, and least ambiguous expression is:
Similar to a traffic officer ordering motorists and/or pedestrians to no longer move forward.
It appears that the hand signal is not unequivocal worldwide.
An outstretched arm, palm facing forward, for example, means “stop” in most Western cultures, but in Iraq it’s considered a sign of welcome.
Nowadays, many will simply accompany the hand gesture with the sarcastic expression
Talk to the hand
Wikipedia: It is usually accompanied by the gesture of extending one arm toward the other person, with the palm of that hand facing the person being insulted, in the manner of the gesture to stop.
"Put up your hand" is the most common expression when indicating "no" or "stop". "Put out your hand" is also common.
In an Ngram search for "officer put up his hand" vs "officer put out his hand", the two expressions have the same number of hits, but almost all hits for "put up" have our target meaning of "no" or "stop", whereas most of the hits for "put out" have a different meaning.
flash your palm at someone
When you flash your palm at someone, you want them to pause or stop. Do this while anyone is speaking and they will almost instantly be quiet. The gesture holds a lot of power so when done willynilly especially during conversations, you might come off as very rude. In the context of interrupting a conversation, it could also mean ‘talk to the hand’ which is a way to dismiss someone mid conversation.
Click on the link to see all the gestures.
lift extended arm with palm facing outwards
Most of these existing answers at the time of writing tackle the meaning of an outstretched arm/hand rather than directly answering the question 'Is it natural to say "put out your hand to say no"?' In Br-E the direct answer to the question is 'no'. It's not natural, or normal, for anyone to say such a thing. In fact it's normal and natural to say 'raise your hand to say yes', notice the difference though between raising 'your hand' which means above your head Vs 'put out your hand' which seems to suggest holding the hand out forward, The photograph in the question seems strange even as a hand signal to stop as such a gesture would not usually be made with splayed fingers.