Your automatic will do just fine if you drive it with a modicum of common sense. First, take it out of overdrive both up and down hills. Don't go up the hill like you're racing at Pikes Peak and drive so the trans isn't continuously down and up shifting. On downhill runs you'll get some engine braking in straight drive. Don't ride the brakes but let the car speed up then brake down to a lower speed. Riding the brakes will overheat them and you'll be at the bottom of the canyon or have a brake/tire fire. Braking down and coasting allows the brakes to cool in between applications. You can use low gear either way but remember you won't set and land speed records in that range.
BTW, I learned to drive in the mountain canyon roads in Northern Utah.
Changing to a manual is far too expensive and requires a ton of fabrication or swapping in a SHO subframe and powertrain. You would be better off buying a different already stick equipped car.