drilling a hole will not destroy the axle, even a 1/4 hole or bigger.
Be sure that the water is getting in from rain and not from that time when the axles were completely submerged under water. In either case you do need to get the water out as it is rusting from the inside. A drain hole is nothing compared to rust.
Running brake wires on inside or outside doesnt matter. They are protected from stuff on the inside but obviously could be sitting in water. New wires, no matter composition, should be water proof enough to work.
BTW, brakes are not grounded so you need positive and negative wires run to bakes, never ground the negative to the frame, and there is no positive or negative on the brake, either direction works - it is just a little magnet you are powering up.