You can use this Instructable to clean a headphone jack, or almost any type of circular jack that size.
-Knife, or something to cut with
-Device that the headphone jack is on
!!!!!!!WARNING: TURN THE DEVICE OFF BEFORE BEFORE TRYING! I'M NOT RESPONSIBLE FOR ANY INJURIES!!!!!!
Step 1: Cut the Cue Tip
Step 2: Dip the Cue Tip
Step 3: Cleaning the Jack
Then, let the jack dry and, there you go! One clean headphone jack.