I don't like the word "fap".
The word is too soft sounding. Considering the activity it needs to be a hard sound. Something with a hard letter, like a K.
Wank or Jerk is better.
At which point "No Jerk January" sounds better, or "No Wank Wednesdays".
This is also the laziest non-masturbatory challenge too.
Put it in the shortest month of the year, because you can't possibly handle 30-31 days.