There’s a couple of different ways you can accomplish this, i think.
Firstly, try out Wave Warp, which also produces a nice wiggle.
However, this option will end up with the string getting thicker and thinner in different places. Alternatively, you could set some extra, different keyframes of the path and then use Time Remapping to randomly jump between those keyframe. You can’t apply the Wiggler directly to the Mask keyframes, but you could use it to on the Time Remap keyframes to control their spacing.
Hope that helps
Graham
http://www.qcit.com