If you do this every move of the game the variant is known as Refusal Chess. Not sure if this will have a smaller first-move advantage than orthodox Chess, though.
If you do it only for the opening move, it will have little effect. The second-best move has hardly less advantage for white. The 'pie rule', where the second player can swap colors if he wants after seeing the move chosen by the other player, is always perfectly fair, though.
We all know that the first player who make a move have an advantage. Beside from a chess variant where one player chooses a first move while the other chooses a color this is the only thing I can think of on how to make the game balance. This is Yes or No Chess. The rule is simple. A player declare a move and the other player will choose if he accepts it and says "Yes" or revoke it and says "No". If he said "Yes", the player will move the declared move. If he said "No", the player will choose another move but this time the opponent cannot decline the move. The process goes alternate.