I hold a cube in my fingers and wiggle it around until enough has come off. Then I refreeze the rest... I've never noticed ill effects on my fish from this. The water is pretty warm, and the food is pretty small, so it's a good temperature by the time they actually eat it. In fact, I have one angelfish that will eat directly off the flat pack when I stick that in there, she doesn't seem to mind that it's cold.
I tried the cup method once, and I refroze the leftovers (my fish don't need a whole cube), but I think I defeated the purpose afterwards. I broke the frozen puck and held a piece of the food-ice in the water until it melted. I think it's easiest to just wiggle around the frozen cube/frozen flat pack.