If Wrangel replaced Denikin as head of Southern Army at the day of its formation (january 1919, so you're a bit too early), it affects little whether he or Kolchak is nominal head of White Movement. Both armies operated completely independently.
Denikin was not a bad military commander per se, but he failed when confronted with enormity of challenges he faced as leader, especially when concerned with issues beyond immediately military.
Wrangel on the other hand, was far more sophisticated man, more charismatic. For example, once when he captured large numbers of Boslheviks, he executed the officers but successfully convinced the low ranks to join him - Denikin would just have everyone shot. Wrangel was far better with civilian side of things, had better control over his troops who under Denikin frequently looted and organized pogroms. Wrangel would more often than not execute people only after trial, which made his rule more lawful than Denikin who was more akin to an arbitrary warlord.
He was just plain better leader and administrator than his predecessor, he just came too late, Denikin resigned because he saw war as already lost.
If you entirely skip the period of Denikin's mediocrity, and do so that early on, you give Whites very good chance to win.