Perhaps the 2nd Final Smash could be called a Final Form. (Still haven't thought out a really good name for it)
Suggestion 1: Players will be able to assign one of the two Final Smashes from the character selection screen after choosing the character.
Suggestion 2: There could be a different Smash ball that allows their Final Form to occur.
Here are A few examples:
Final Smash: Mario Finale
Final Form: Super Mario (improved power, higher jumps, glide ability, bigger or rapid fireballs and most attacks does flame damage)
Final Smash: Hyper Flame Breath or giant Fire ball
Final Form: Giga Bowser
Or if Ryu manages to join the fray
Final Smash: Shinkuu Hadoken or Metsu Shoryuken
Final Form: Evil Ryu
I would put Megaman but I have not played many games within his series