Does touching shoes with the back side of my hands or fingers or the part of my arms right above my wrist have the same din as touching them?
Answer:
If your hands (below the wrist) touch your shoes, even the back of the fingers, this has the same status as the front of the hands.
Best wishes.
Sources:
The halachah of touching one's hands is a halachah of the hands (yadayim). Therefore, if any part of the hands touches shoes, they should be washed.
Best wishes.