I'm betting that most people know exactly what I am talking about. It happens when you're scrolling through some social media and you see something that is only a little funny. It may catch you by surprise. It's a single utterance, a single, quick, guttural exhalation, typically through the mouth, but I can imagine that for some it goes through the nose. I would consider it a type of laugh, but JUST BARELY. I hope this makes sense as to what I am saying.
Now, which words don't work. First there is "giggle". Giggle goes well beyond this laugh. The OED defines giggle as:
To laugh continuously in a manner not uproarious, but suggestive either of foolish levity or uncontrollable amusement.
"Chuckle" is close, but the definition appears to assign a higher level happiness than the word I want. The OED gives the following definition:
An act of chuckling; a laugh of triumph and exultation: formerly applied to a loud laugh, but now chiefly to a suppressed and inarticulate sound by which exultation is shown.
The problem I am having is with "exultation is shown." The OED definition of exultation is:
The action or state of exulting or rejoicing greatly; triumph, joyousness, rapturous delight; an instance of the same.
And, this is very slight amusement. It is definitely an inarticulate sound, but it is not suppressed, and sometimes, oftentimes, amused contempt or disbelief is shown.
"Snigger" is defined as:
To laugh in a half-suppressed, light or covert manner; to snicker.
This makes me think of how we used to laugh at things behind our teachers' backs. "Teehee", "twitter", "titter", "snirt", "snirdle", "sniggle", "snitter", "snicker" and "whicker", all talk about laughing in a suppressed manner. This is not a suppressed laugh, it is a laugh that just BARELY gets out. "Neicher", "nicher", or "nicker" appear to be regional synonyms of snigger.
The closest word I know of is "chortle". The OED gives the following explanation for chortle:
A factitious word introduced by the author of Through the Looking-Glass, and jocularly used by others after him, apparently with some suggestion of chuckle, and of snort.
So, if Lewis Carrol created the word, how did he use it? The quotation given is:
‘O frabjous day! Callooh! Callay!’ He chortled in his joy.
The most recent quotation, for some reason (on other words in the OED, I have seen quotations from as early as 2007), goes all the way back to 1889 in The Referee which I THINK is the Weekly Referee. The quote is:
Many present on Boxing Night fully expected that when he appeared he would chortle a chansonette or two.
"Chansonette" is French for "little song" or something like that. If you can chortle words, this does not fit. There are 4 other quotes, and I can do all of them and explain why they do not fit (or in one case no context is given; and no year is given for the paper, so I don't know how I'd how I'd find the paper). If someone is interested in that let me know (everyone in Colorado gets the OED free through the Denver Public Library), but I fear that may get tedious. If someone wants the other 4 let me know in a comment. For now, I will assert that it doesn't fit.
No other laugh synonym comes close. For example, neither "keckle" nor "cackle" work, both share the definition,
A short spasmodic laugh; a chuckle.
"Chuck", an obsolete synonym for chuckle that died out almost 400 years ago does not work when looking at the example quotations given, such as one talking about your shoulders being sore after. "Shuckle", another obsolete word seems to be a synonym of chuckle. "Yock" means,
A laugh, esp. a loud or hearty one; a burst of laughter.
A colloquial synonym for laugh is "hoot". The only definition given is "to laugh". In my experience, however, hoot is used to describe more rambunctious laughter. "Guffaw" describes a boisterous laughter. "Gawf" is "A loud noisy laugh". "Roar" doesn't fit for obvious reasons. "Ha ha", "haw-haw", "hee-haw", and "yaw-haw", all describe loud laughs (they're all in the OED). "Horse-laugh" is "A loud coarse laugh". "Split" can mean to laugh uncontrollably, while shake can mean to shake with laughter. "Kink", means "To laugh, esp. immoderately or uncontrollably" and appears to not have been used in more than a hundred years. "Roll", which dates from 1819 means to move about with laughter. "Pee" can mean to pee with laughter. NONE of these fit, and I cannot find any other synonyms.
If there is no specific word for this, I think "chuff" should be used. Big cats, tigers and lions (but not mountain lions, they purr like housecats) make a similar noise when they are happy (analogous to cats purring). It's not exactly the same. Obviously, a lion has much more bass when it chuffs, and tigers sound like they're rolling their "Rs" when they do it, and they repeat the sound, but still, I can't think of any other word that describes this better. But that is why I am here. Is there already a good word for this that I have missed?
UPDATE ON THE ANSWERS
While I do greatly appreciate all of the answers and engagement, none of the answers given fit exactly, for a variety of reasons.
First, this is not a "snort", as a snort is through the nasal passages. While I am sure that some people do snort in the same situation when I would "chuff", this is NOT a nasal exhalation (upon further thought, maybe I do snort in rare instances, such as maybe if I am eating or drinking something when the humor hits me). Secondarily (not quite as important due to the flexibility of language), snorts are typically more forceful and audible than this. Finally (again not too important due to language plasticity), in my experience, when someone "snorts with laughter" or "snorts in amusement", this typically refers to loud, uncontrolled laughter that results in accidental, usually embarrassing, snorts.
"Half-chuckle" is pretty close but, given the examples provided, half-chuckle seems to either have have a similar connotation as snicker, in that it is a suppressed laugh, or it appears that the connotation is a forced, insincere laugh. Again, due to the flexibility of language, this may be the closest, though.
"Huff" is also close, as it is almost an oral version of snort. However, huff already has a negative connotation to the word. The OED's earliest definition of huff, dating to 1582, simply means "to blow"; however, in 1599, it took on the alternative meaning of:
A fit of petulance or offended dignity caused by an affront, real or supposed; esp. in in a huff, to take huff.
So, the connotation of huff is the opposite of what I am looking for. Again, I know this sounds like a broken record but, due to language's impermanence, this is only a small problem.
"Chuff", at least all of the definitions I can find, refer to the loud, regular bursts of steam emitted by train engines, thus, it's onomatopoeic. This suggests a much louder exhalation.
"Puff", again, is very close, but there are some issues. First, I checked the OED, MWD, Dictionary.com, and Google, and none of them mention any kind of jocularity in reference to the word. And only one of them mentions its use in scorn or disdain. Also, so far as I can recall, whenever puff is used as a verb to describe some sort of communication, it had a negative connotation, that the speaker was somehow upset.
The person who mentions the word "scoff" explains why it does not fit.
"I blew air through my nose" fails because, first, it is a 6-word phrase. Second, it is a synonym for snort, and again this is oral.
"Perfunctory laugh" does not work because the amusement is genuine, but it is also close, because perfunctory can also mean "superficial, trivial".
"Bark" does not work, because it suggests a "loud" noise.