When exporting blendshape animation to FBX from Maya, we just need the curve information and none of the vertex delta information. How can one get just the animation data into FBX and then UE? This would reduce FBX file size and eliminate unnecessary data. I imagine one would need to store the animation channels on a joint and then write something to read those custom attributes and apply them to the blendshape.
from blender you can add anim curves with my plugin:
http://mosthostla.com/gamedev/ue4curves/
I would suggest you just import the FBX with just the bones. Add the curve data you want to an extra bone you can then remove.
Move the curve data you want, delete the extra bone, and re-export for UE4.
Surely you can do this directly from Maya. I have just never tried it. I probably should since I own it, Probably the next project 
Yes it’s easy enough from the DCC side, I’m mostly wondering the workflow from the Unreal side.
On the unreal side the curves are just data.
you can use them from the anim graph to power just about anything.
common things are probably foot/hand IK, root rotation for turn in place, fall/movement ranges for predictive animations, weapon/actor local space rotation/transitions (think of the rotation you need to apply to a blade when you unsheathe it), material effects like glowing eyes, or morph targets or blend shapes that need to progress with an animation (elbow adjusts?).
in anim BP you can just “get curve” and pop in the correct name to get the value or the curve whenever it is executed.
How you use this is where things get complicated.
I exported the blendshape animation as custom attributes on a bone and Unreal seems to automatically apply them to the blendshape. So I guess it maps it automatically by name.