Hmmm... I kind of look at it differently. Link and Zelda have their pieces of the Triforce because Ganondorf- a person with an unbalanced heart- touched the Triforce and caused it to break in the first place. I don't necessarily think that the pieces of Wisdom and Courage went to Zelda and Link because they already possessed these traits; I think it's mainly because they are simply chosen by destiny.
For fragments (Power, Wisdom, Courage), I honestly think anybody could have them. The main issue is coming to possess the Triforce in its entirety. Nobody really wanders off in search of the pieces save for Ganon in his attempt to obtain full power or (one of the many) Link because Wisdom or Courage got shattered in an effort to be hidden from Ganon.
What further makes me believe this is how the Triforce of Wisdom was passed down through generations in the Royal Family. There are a couple Princess/Queen Zeldas in between OoT and TWW who don't play any important role in history, so I doubt they were able to keep the Triforce of Wisdom because they were worthy. I think it's just because it was handed down. Likewise, I think if it was necessary, Link could pass it down to his descendents or even to a trusted friend. I don't think there is really anything keeping anybody else from obtaining one of the pieces, really.
So, I think the only issue in being able to hold the Triforce comes around when the Triforce is whole; balanced ("True Force"). When it's in this state, one has to have a balanced heart. Princess Zelda (as Sheik) in Ocarina of Time begins a speech with Link with, "If you would seek the sacred triangle, listen well..." So I think she is implying that Link is able to hold the True Force... believable, since he's a pure hero. Likewise, the King of Hyrule was able to touch the "True Force" and have a wish granted without it shattering, but that might just be because the pieces were finally collected. As said by legends, you're gonna have to have a good, balanced heart to hold the Triforce.
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So, to reiterate, I think pretty much anybody could obtain Wisdom, Power, or Courage piece of the Triforce on their own. However, now I will try to get to answering the actual question of the topic better... Forgive me for blabbing too much. If Ganon touched the Triforce and it split and Link and Zelda did not exist, I think it could go a few different ways:
Courage: I see Rusl holding this piece. He's a strong, brave family man. He's protective of his village. Even after being wounded, he still stands to protect. I mean... he stands up against a wolf! That is a brave, brave man. If not him, then Ashei. She seems like somebody who'd never give up and be able to do things on her own if she needed to. Outside of TP, I'd probably go with somebody like Mikau, who put his life on the line (and lost it) for the love of his life.
Wisdom: Shad!.... not. Being wise and being smart are two different things. Shad's booksmart, very booksmart, but he's not the wisest fellow, and I felt like I needed to put that out there. I'd really go with Impa- OoT version. When we meet Sheik, s/he's becoming much wiser than s/he was as a young princess. Who do you think s/he learned everything from? Impa is a very wise character and passes that on to both Link and Zelda, which in itself is a wise move. And then there's an obvious choice- Sahasrahla. I don't think he really needs an explanation.
But that's if Ganondorf touched the Triforce and busted it up. What if somebody else with an unbalanced heart touched it and it shattered and Ganondorf didn't exist? Who would the Triforce of Power go to if Link and Zelda didn't exist?
Power: I'd like to say Midna. Why her? Because power doesn't necessarily have to carry negativity. Midna is a powerful ruler who ventures outside her own realm to save her kingdom. She may be snarky and selfish at first, but she grows. In any case, she's a powerful being all together, from personality to actual magic. I might also say Nabooru, because she already assumes the role of Second in Command of the Gerudo even as a child. She had strong leadership skills and her sense of independence and values in right and wrong are definitely what helped her take a stand against her own king. That might also fall under courage, but I think her leadership and ruling skills are what make her lean more towards power.
(thank you so much if you actually bothered to read all that T_T )