Term for a snort that is almost a laugh

Solution 1:

whicker |ˈ(h)wɪkər|

verb [ intrans. ]

1 utter a half-suppressed laugh; snigger; titter : a half-loony whicker of nerves.

• (of a horse) give a soft breathy whinny : the palomino whickered when she saw him and stamped her foreleg.

2 move with a sound as of something hurtling through or beating the air : the soft whicker of the wind flowing through the July corn.

noun

1 a snigger; a soft, breathy whinny.

2 the sound of something beating the air.

Solution 2:

It's slang, but there is the word snortle. It's defined as:

A hearty laugh that is punctuated by a snort on the inhale.

Or the Wordnik entry has it defined as:

To snort; grunt.