Use 'snigger' to describe a quiet laugh that can be rude or mocking. He tried to hide his amusement by hastily turning it into a cough, but his snigger was heard by everyone.
Pro Tip 2/3
Subtle Mockery
'Snigger' often implies laughing at someone without them knowing, in an unkind way. The students exchanged looks and began to snigger when the substitute teacher misspelled a word.
Pro Tip 3/3
Not Overtly Loud
'Snigger' means the laughter is quiet, possibly hidden, unlike a loud guffaw. Sarah had to bite her lip to stop herself from letting out a snigger during the solemn ceremony.