If I had to find a solution to this, with no alternate approaches re. the drone size & capacity etc., I'd find a PSU with something above the maximum rating needed (or two or more that are designed for load sharing) and split them at the DC bus after the rectifiers and smoothing.
Keep the rectifier/cap part on the ground and the converter part in the drone, with some extra HF caps at the converter input, and run the system at near its maximum AC input voltage to keep the DC bus voltage well up, 300 - 500V or so.
That means the link cables are only carrying somewhere roughly around 8A - 13A at 4KW converter input (200A 20V out, less inefficiencies).
Quite a bit of weight in the drone, but I'm pretty sure a fraction of the weight of long 200A tether cables!
However it is a lethally dangerous setup with the high voltage, high current DC link and it's not something for a beginner to consider, or suitable for use outside a restricted area.