I never cut them up unless I’m in a mad rush and sticking a potato in the microwave in an “emergency” (you know those potato emergencies right?)
I saw a technique a while back the suggested making a shallow cut around the equator of a whole potato, then steaming or boiling (or my personal favorite, pressure cooking) – once done, twist gently in opposite directions and the skin pops right off. Tried it, it works perfectly.