When i am going down a STEEP hill, my weight is more forward. More forward weight means more pressure on the hands.
If you brake on the hoods going downhill, try to scoot back a bit in your saddle and put some of your weight back further on your pedals instead of onto your hands.
Ideally, you should be braking in the drops on very steep downhills-- because you have better steering control in the drops, you have a better grip on the bars, and generally your hands on the hoods are further forward than when in the drops thus making the weight forward issue worse.
Try sitting further back in the saddle and transferring some of your weight onto your pedals. Shift your weight backwards off your hands.