Learn English – Term for a snort that is almost a laugh

A trial balloon is “an idea, suggestion, or prospective action, product, etc. offered to an audience or group in order to test whether it generates acceptance or interest”. A trial balloon can be generated sort of secretly or deniably via a planned leak. A related term is stalking horse, “A candidate put forward instead of any of several potentially successful candidates in order to initiate a leadership debate, gauge feelings, divide opposition etc.”

I would probably use amusing for this. From your description, I'm imagining a story or something else that is entertaining and has a humorous tone, but there's no one specific thing or moment that makes you laugh the way that the punchline of a joke does.

There are some more specific words that apply to certain cases. For example, this is how I usually think of the Mel Brooks film The Producers, about two men running a scam that involves producing the world's most terrible play - it's not funny because of jokes or one-liners, but just because their situation becomes increasingly absurd and ridiculous. In this case, the word farce fits well.