If I had to, I would switch out Tobirama. My guy would still be Hashirama's brother who created the Impure World Resurrection technique (where did edo-tensei come from?), but it'd be a bit different.
His name would be Uric (cause it's somewhat oriental, but still close to my name

) and he would be famed for his incredible chakra control, which is so great that he not only could walk on walls and water, but also air. He could form his chakra into arms like Bee and Naruto (though not as powerful, obviously

) and his varied chakra affinities (which only excluded water) helped spawn many techniques still used by Leaf shinobi today. He also had a natural curiosity for kinjutsu, which is how he got the idea for edo-tensei. He, unlike Tobirama, actually mastered it, but refused to use it due to the sacrifice it requires. All other parts of the 2nd's history still apply.
Now THAT'S a kick-ass hokage
