Blender isn't storing these normals for each shape key, so its not simply a matter of accessing some data.

While you could calculate them yourself, this isn't very convenient.


Temporary Mesh
====

- Pin the shape key so its active an no others are taken into account.
- Read the mesh using the `Object.to_mesh` method.
- Read the normals from the mesh.
- Remove the mesh.



Existing Mesh
====

- (optionally) store the vertex coordinates.
- temporarily apply the shape-key to the mesh.
- calculate the normals.
- read them from the mesh (can store how you like, but be sure to copy them so as not to hold a reference to the original mesh data).
- restore the original coordinates and optionally re-calculate normals again<br>*(though this could be postponed until after you're done with all of the shape-keys)*.