I took @AlanSE's advice and downloaded Audacity and did a number of measurements.
There are some challenges - what is the snap in the snap? Does it start with the sound of your finger gliding over your thumb, and where does it end? I recorded my snap under definite sub-optimal conditions, using the built in microphone of an iMac inside a 14x10 office with plaster walls - it was hard to tell where the snap ended and the echo began.
And even so, as with @Lelesquiz's snaps above, there is a definite, very short primary sound that is much louder than the secondary reverberations which go on for quite some time. See below:
So I decided to go empirical - if I listened to an ever shorter section of the snap, at what point did it cease to sound like a snap? I was surprised to hear that even at 1/1000 second it is recognizable as a snap:
Here is the monster MP3 exported from the 1 ms selection above (1579 bytes including useless tagging info): https://dl.dropboxusercontent.com/u/117024/etc/MilliSnap.mp3
So to answer my own question: "A snap" is roughly 1 ms.