  This is the second paper in the series to study the initial perturbation of
mean curvature flow. We study the initial perturbation of mean curvature flow,
whose first singularity is modeled by an asymptotic conical shrinker. The
noncompactness of the limiting shrinker creates essential difficulties.
  We introduce the Feynman-Kac formula to get precise asymptotic behaviour of
the linearized rescaled mean curvature equation along an orbit. We also develop
the invariant cone method to the non-compact setting for the local dynamics
near the shrinker. As a consequence, we prove that after a generic initial
perturbation, the perturbed rescaled mean curvature flow avoids the conical
singularity.
