Actually dragging (or wheeling in) a wire or having a wire car supplying the plane with electricity during takeoff would work too.

After doing more of the math, I realized that the energetic cost of takeoff is quite a small fraction of the overall cost. So the only real benefit of the catapult would be to reduce the size and weight of the propulsive machinery on the plane. So externally providing just the electricity wouldn’t be much of a benefit.