How to keyframe bezier handles for individual points on a spline?

So I have made a telephone cord that runs out of a phone handle and to the phone base.

I have animated the handle moving out of its cradle, and I have managed to use expresso via a point node to attach the points of the spline I need to move via some nulls.

With that complete, I now need to be able to keyframe the bezier handles of the spline points, so that there is realistic curvature in the cable.

Is there a way to do this?