The way your saying things sounds like Sasuke is wiser and smarter than Hagoromo. Up until now, Sasuke never thought of anyone but himself. Many people have thought of a way to find peace and you think that Sasuke will come up with an answer just like that?
If anything, peace will be achieved through cooperation. Not just from Sasuke and Naruto, but from all the other Shinobi. No one man can achieve peace, if the majority isn't willing to cooperate. That was what went wrong with the sage's ninshuu belief and with Hashirama's shinobi system. They both tried to do things on their own.
So, I don't think Sasuke or Naruto can come up with the answer alone.
Please read my theory again. It clearly state that neither will create peace alone, it states that one will understand how peace is obtained while the other will make it a reality. Sasuke is the Spiritual part of chakra, while Naruto is of the physical part. Spiritual as in the idea and physical as in the realization of an idea. ( Its the explanation of Creation of All Things. ) I am not stating that Sasuke is wiser or smarter than Hagoromo, I am stating that he has had a different past and thus have a different and perhaps better understanding than Hagoromo.
Say if I were to give two people a problem to solve, but I gave one person more info on the problem than they other. They can both be equally smart, but the person with the most info has the highest chance of succeeding. ( That is what I mean with Sasuke understanding something Hagoromo did not. )
Also, please state a single area or action where Sasuke has done anything because he "only cared for himself".
Sasuke wanted to take revenge on Itachi because he cared for his clan and family, Sasuke wanted to take revenge on Konoha because he cared for his family, clan and brother and now he wants to change the shinobi system because the cares for his clan, his family, his brother and a majority of the world. He said so himself, he doesn't care what happens to him as long as his goal is reached. Someone who only cares about themselves wouldn't say that. Sasuke also have always stated that he will
not kill anyone other than his targets along as they don't step in his way.
In other words, the fanbase has always been blind to the fact that Sasuke isn't selfish or as cruel as they want to make him. I am not saying he is a loving, caring dude either. He clearly mainly cares for his goal, but he cares very little about himself. ( He has always been like that, even since he was a little kid. )
Sasuke is a person with no care for his own life as long as his goal is reached, he said he would gladly give up his own life if it meant that his goal was reached. Now how can you say that he only cares about himself? Its more correct that he simply doesn't care about others alot, which was shown when he stabbed Karin. ( Though he has changed since then. )
I seriously doubt that Sasuke will get killed. Naruto never goes back on his word and he promised Itachi that he wouldn't kill Sasuke.
So, if Sasuke comes up with the answer and Naruto will execute it, doesn't it mean that both Sasuke and Naruto will achieve peace? But if you really think Naruto will kill Sasuke, then you really don't know Naruto's personality. Also, Kishi doesn't want Naruto to kill. That's been made painfully clear.
I just think that Sasuke will cooperate by helping Naruto, just like his other friends will help him achieve peace. If both Naruto and Sasuke comes up with the answer, the prophecy wasn't needed.
You see, here is where I have a major problem with Naruto's character. He promises Itachi that he won't kill Sasuke, yet Naruto had already told Sasuke that if they fought then both of them would die there on the battlefield. Meaning that Naruto would have killed Sasuke and Sasuke would have killed Naruto, he said that himself. So, he said he would kill Sasuke if need be, but he would die too and later he promised Itachi that he wouldn't kill Sasuke.
Another problem with his character is that its exactly the same as Hashirama's. Hashirama never wanted to kill Madara, but he had no other choice. You said that Naruto will never go back on his word, well he made two promises. One was to never kill Sasuke, the other was to find peace. But what if the only way to peace is through killing Sasuke? What will he do then? Fail both promises or only do one of them? Either way, his character will be broken. The series will either end with Naruto dying, leaving Sasuke to be the one to create peace or Naruto will kill Sasuke and create peace, destroying his character completely.
You also have the possibility that Sasuke will cooperate with Naruto, but that wouldn't really work out either. Mainly because everyone hates Sasuke, and then the story would repeat itself as it did when the first Hokage was going to be selected and Hashirama wanted that to be Madara. However, no one supported Hashirama on that and Madara left the village.
If Sasuke is magically forgiven by his sins, then the story would be lacking and turn rather bad. He tried to kill the Kages, that is the same as Madara did and more or less succeeded at. Would you say that the world would forgive Madara now if he simply said: "Well, I don't wanna go through with my plan anymore so I guess I will just live my life in peace now." No, they wouldn't. Sasuke won't be forgiven simply by helping in stopping Madara, he will still be hated and feared and when that is still an element, peace cannot be achieved. That is why the most likely scenario is that Naruto kills Sasuke. Upon doing so, Sasuke will leave the world with all hatred pointed towards him, ending a strong lineage of hatred.
That will also break Naruto's character, and allow for a new version of him be "build". You see, Naruto's character is as one-minded as Madara and Obito's. They are all shallow characters in the form that they don't give a damn to understand the other person, they only do and follow what they believe in. That will never create peace, understanding will create peace. Sasuke's only wish to to fully understand, Naruto only wish for peace without understanding it.