Both snigger and snicker mean the same thing - "to laugh in a covert or partly suppressed manner: titter," say editors of Merriam Webster Inc. "Snigger" is essentially a modified version of "snicker." In this case, the onvoiced "k" sound in "snicker" has been altered to the voiced "g" sound in "snigger." (A "voiced" sound is one that is made with the vocal cords vibrating.)
Both "snicker" and "snigger" are imitative and expressive in origin. They are imitative in that the initial "sn" sound, like that in words like "sniff," "sniffle," "snort," "snivel" and "snarl," is suggestive of the sound made in performing the action denoted by the verb. The final element, "-er," occurs in many words descriptive of sounds, such as "clatter," "sputter" and "whimper."Neither "snicker" nor "snigger" is more appropriate than the other - they are equally acceptable.