The hands are focal points for the energy, however, Reiki does not depend on them. In my mind the hands symbolize connection. Connecting to Reiki is enough. How else could one treat or attune from a distance?
You may be overthinking things a bit, but then I am not sure what your teachers told you, so if I am out of bounds please disregard what I'm writing.

That said:
1) Just cup the cut fingers in your other hand and let Reiki flow.
2) It doesn't matter. 1 hand, 2 hands, or no hands. The feeling of connecting the reiki energy to the affliction is enough.
In the case of the tiny spot. Do whatever feels right. I would lay my extra hand on my upper thigh I think If I was unsure where to put it.

I would not "de-activate" anything.
In my mind reiki flows throughout the entire body. As I said the hands are just convenient, comfortable means of connecting. People tend to look funny when you do reiki with your feet, knees, or your nose. Hands are accepted points of contact in a healing modality.