I'm actually curious not about your hand width, but the angle between fingers 1 and 5. Both the photos of your hand positions show almost a V-shaped angle made by your thumb and pinky (if you imagine imaginary lines running down the thumb and pinky and meeting in the middle of your hand). To get maximum reach, we want as close to a straight line as possible.
It's hard to tell only seeing the position from the top. Most of us have more reach if we round the hand by lifting the large knuckles slightly. In this position, spreading the fingers increases the angle of fingers 1 and 5 towards a straight line. Again, it's hard to tell from the photos, but I wonder if your hand may be flattened out, so that the large knuckles and palm are almost touching the keys? In that position, spreading the fingers actually causes them to reach up toward the ceiling, which doesn't help with horizontal reach on the keys. That means that with a flat hand, getting fingers 1 and 5 into a straight line is next to impossible. Then, people start pulling their hands toward themselves so that they are playing only the very tips of the keys. This does keep the palm off the keys but it reduces the options for sound quality (as well as the ability to hit black keys.)
In a rounder position the hand really has to be above the keys, not in front of them. You will be making a very long, low archway above the keys, instead of a V in front of them. You may find yourself hitting extra notes as you get used to that. But in the long run you'll develop a wider reach--and the whole white vs. black key issue won't be an issue at all since you'll be working much closer to the black keys.
Good luck! Enjoy the magnificent Brahms!