Depends,
if the "snake-curve" is NOT weighted to joints (or influenced by any other deformers), you may be able to achieve the effect you're after with a "Wave Deformer". (under Animation / Create Deformers / Nonlinear > Wave) Just drag the deformer, or scroll the Offset attribute, to have the mesh (or Curve) deform.
If your mesh's deformation is already influenced by skinned weights (i.e. joints);
create your curve path, then geometry constraint the joints (or relevant control nodes) to the curve.
Hope this helps.
-ΦZ