Who chooses the targets for Captain's Maneuver?
The controller of the spell (who is the person that cast it) gets to decide which creature's damage is replaced, and where that damage goes.

When you cast a spell, you choose the targets for that spell. In the case of Captain&#39;s Maneuver, there are 2 targets that you choose. One is the creature that would receive damage, and the other is the creature that receives the damage instead. This works the same with Captain's Maneuver as it would with any other targeted spell such as Lightning Bolt.


  
  Casting Spells
  
  
  
    601.2. To cast a spell is to take it from where it is (usually the hand), put it on the stack, and pay its costs, so that it will eventually resolve and have its effect. 
    
    
      601.2c The player announces his or her choice of an appropriate player, object, or zone for each target the spell requires.