Have you tried using Body Mode within the Character Story Track?
Put your full body animation into a character story track (we will refer to this as "FullBodyTrack") and then create another character story track that contains the data for the hand animation (we will refer to this as "HandTrack"). Do this in order - Add the FullBody Track and it's Take Data AND THEN create the "HandTrack" and add it's Take Data.
Change the character in the HandTrack to match the character that is in the FullBodyTrack, this is done via a drop down list next to the word "Character" within the Character Track.
Next, look for the little white figure icon next to where you just swapped your character - clicking this will open the "Body Part" window.
Deselect Full Body and then check "Right Hand" and "Left Hand" - this will allow the data to only affect those specific body parts.
As long as the HandTrack is below the FullBodyTrack in the story window - this should work.
If you want to ONLY have the finger data and not the wrist than you will need to remove some objects from the "Track Content":
- In you "HandTrack" click on the dark grey box next to "Track Content"
- Remove (one by one😞) any Controller that affects the Right and Left Hand (careful not to remove the index, middle, ring or pinky finger controllers/effectors for each hand).
This should do the trick.