New Delhi, India — At the top of the world amid pristine white glaciers and towering rock, silence reigns. Suddenly it is broken by a ladder falling from the sky. Milan Pandey is sitting back down at Everest Base Camp, looking out over views that few have ever seen — and he got there without having to pull on a crampon or wield an ice ax. He is a drone pilot, and his work may change things on the world’s highest mountain forever. The ladders, ropes and oxygen cylinders that Pandey can transport via drone to aid the Sherpas or...