I’m not quite sure from your phrasing if we’re actually disagreeing, but… I’d argue that Muttley’s laugh is just about the perfect demonstration of sniggering… a sort of contemptuous snorting giggle that would accompany the latest spectacular failure of Dastardly’s foolproof plan. (And that Scooby’s laugh is more of a snicker… just because Scooby is nicer). 
NZ English is heavily UK based but with a strong US influence (pretty much post-WWII) from the entertainment industry… snigger seems completely normal and harmless to me (with no other connections or overtones). Snicker is less common (other than for the Mars company’s peanut-stuffed novelty bar) but it wouldn’t seem out of place.
That said, if I saw “snicker” without the context of a laugh I’d probably say it was a reference to a swishing, cutting sound, as in: “The vorpal blade went snicker-snack!”