As you can see, the snake's head also deforms. Is that ok? If your answer is no, then I would suggest reconsidering the deformation method.
What you can do is to:
1. create a chain of joints;
2. bind the snake to that chain;
3. create splineIK for that chain;
4. apply nonlinear Sine (and maybe Wave too) to the curve. You can adjust the intensity and transformes of both nonlinears to achieve the randomness you wish.
Get really familiar to their attributes on a separate object before you do it on snake's spline. For naturalistic animation you might wish to make the head part moving as little as possible.
If you still need more random snake waves then it is possible in many ways, including clusters, blendshapes and dynamic curves. And, more complex shapes you want your snake to be bent means more joints in the joint chain, not less than 10 anyway.
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Maya2019.1 @ Windows10 & GeForce GTX1080Ti
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