Skill Awakening is a procedure that replaces max-level skill of an Awakening unit with different skill (unit-specific), or replaces that skill with max-level skill unit had first if you for any reason decide to go back on it. It does not happen automatically upon Awakening, you will need to initiate the procedure yourself (and spend same resources unit needs for Awakening, with different fairy (Naiad, SAW fairy, is a drop from new weekend daily)).

We actually already have it, for Black rarity units. Head to Awakening page in game and press "Skill Awakening" button there