In my experience the verb 'bat' is often used for this:
The cat is batting the decorations hanging from the Christmas tree.
https://en.wiktionary.org/wiki/bat#Verb : (intransitive) To strike or swipe as though with a bat.
The cat batted at the toy.
As noted by others, pawing is also a descriptive choice.
I would recommend either verb over punching (typically a more forceful action which I associate more with humans than cats).
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The first word that came to my mind was swatting .
https://en.wiktionary.org/wiki/swat#Verb , with the given example
The cat swatted at the feather.
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Punching involves bending the arm and striking out forcefully with the closed fist.
A cat can't make either of those movements in the way a man would.
A cat playing with a dangling object usually bats it sideways with its paw.
You could simply use pawing .
ell.stackexchange.com/users/104866/Kate Bunting
One common term for this is batting or batting at .
When used with a cat (or other animal) this means hitting or tapping at something with the paw.
The cat is batting at the decorations hanging from the Christmas tree.
Describing a cat as "batting" or "batting at" another cat or an object means the cat is striking or tapping with its paw, but not so forcefully as to be a violent attack.
It usually suggests curiosity or playfulness rather than hostility.
ell.stackexchange.com/users/11195/barbecue
A very idiomatic way to say this is:
The cat swiped the object with its paw.
As also used in the example by:
Merriam Webster 1 : a strong sweeping blow //
a swipe of a paw Although less reliable, a simple search also yields many results showing it in real-life usage:
Thanks Google
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Taps
It might be an internet colloquialism, but I generally see this referred to as taps.
Many "cute cat videos" describe it as such, and there's even a subreddit devoted specifically to r/CatTaps .
It's worth noting that there is a fair amount of connotation depending on what kind of activity the cat (or other animal) is actually doing.
Tapping Moving the paw towards and away, possibly touching, usually tentative or investigative.
If the tap causes the target to move, might lead to Batting.
Batting
Connecting with a loosely hanging item with each (or most) attempts.
Each successful bat sends the item swinging.
Swiping More aggressive, and generally directed at another animal.
Hissing or growling might be involved.
Claws might be out.
This might be a followup to successfully batting an item.
Pawing
Generally an attempt to retrieve or receive something such as a partially obscured/covered item, or in/near a food bowl when they're trying to explain to their human that it's dinner time.
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I don't think to punch is the right verb here.
Take a look at its definition from Cambridge dictionary: to punch (verb): to hit forcefully with your fist.
She punched him in the face after he called her names.
As cats can't make a fist, I'd advise you not to use it.
Instead, I believe to beat would be a good choice. to beat (verb): to hit repeatedly.
The cat is beating the decorations hanging from the Christmas tree.
ell.stackexchange.com/users/87807/krobelusmeetsyndra
to slap : to hit someone or something with the flat part of the hand or other flat object
https://www.reddit.com/r/CatSlap/
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I agree with the upvoted answer that batting is the best word.
There is another word that works, though it may be a little too cute.
The word is boop or booping .
Here's an example from Reddit:
"Kitten boops himself" :
You can find many more examples online just searching for "cat boop."
If cute is what you're going for, it's a fine choice.
It's not in most dictionaries as it's more of an onomatopoeia.
I think the meaning is basically thinking of the noise that a button on, say, a cute robot would make.
Often it refers to the cat's nose (since that is button-like), but it is not restricted to noses.
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Swiping (to swipe), cats swipe at things.
Could also be: Jabbing Pawing Tapping Poking
ell.stackexchange.com/users/108434/Dominic Ormston
nGrams reveals 'batted' to be the verb of choice (of those thus far presented) - but I think what we can conclude is that the reporting of the actions of cats has increased exponentially with the arrival of the internet... https://books.google.com/ngrams/graph?content=cat+swatted%2Ccat+swiped%2Ccat+batted%2C+cat+pawed&year_start=1800&year_end=2008&corpus=15&smoothing=3&share=&direct_url=t1%3B%2Ccat%20swatted%3B%2Cc0%3B.t1%3B%2Ccat%20swiped%3B%2Cc0%3B.t1%3B%2Ccat%20batted%3B%2Cc0%3B.t1%3B%2Ccat%20pawed%3B%2Cc0
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What is the verb for describing the movement of a cat's paw  when it is trying to hit something with it? Can I use the verb  punch ? For examle:   The cat is  punching  the decorations hanging from the Christmas tree.
What is the verb for describing the movement of a cat's paw when it is trying to hit something with it?
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<word-choice>
ell.stackexchange.com/questions/236804
ell.stackexchange.com/users/60696/Dmytro O'Hope
In my experience the verb 'bat' is often used for this:  Describing a cat as "batting" or "batting at" another cat or an object means the cat is striking or tapping with its paw, but not so forcefully as to be a violent attack. The following verbs may be used: "bat", "swat", "paw", "taps", "swipe", "boop", "jab", ‘poke" or "slap". 
The following verbs may be used: "bat", "swat", "paw", "taps", "swipe", "boop", "jab", ‘poke" or "slap". 