Apart from the approach above, I was trying different routes. What seemed to be promising was this setting (in red) here:
As vertex groups are stored per object, not per mesh, this setting should be an object related setting, too. Therefore, my thought was to keyframe this value object-related, too. I’ve added two vertex groups to both cubes, named the groups “all” and “none” (containing all resp. none vertices). If you set the setting to “none”, it’s like disabling the shape key.
However, this doesn’t work for two reasons: The setting seems to be stored within the mesh data block, which, IMO, doesn’t make sense as data gets inconsistent if an object making use of the mesh does not even have a vertex group with that name. (this is like storing the delivery address in the product table, not in the customer table, so it’s invalid if the “wrong” customer orders the product). The second reason is that the value simply can not be keyframed.
So I’m still struggling with a basic animation task again…