Shikamaru might be the most influential. He is known for his intelligence. In a time travel situation, he could quickly analyze the situation, come up with plans, and predict the consequences of different actions. His strategic mind would be crucial in dealing with any unexpected events during the time travel, whether it's in the past or the future.
Definitely Iona. As an advanced Fog ship that has developed emotions and a sense of self, if she were to time travel, she could have a very unique perspective. She might be confused by the differences in the past or future she travels to, and her attempts to understand and fit in could lead to some really engaging storylines. Also, her relationship with the other characters would be very different in a time - travel context.
Kazama Chikage might be an interesting choice as well. He is a powerful and somewhat arrogant character. If he time - travels, perhaps to a past era where his clan was even more powerful, he could try to change history to make his clan even more dominant. Or if he travels to a future where his power is nothing compared to modern technology, his struggle to come to terms with his new position in the world would be an interesting plotline.
Iroh would be fascinating to see time - traveling. He has so much wisdom already. If he traveled to different times, he could share his knowledge and perhaps change some key events. He could also gain more insights from other time periods, which would further enrich his already deep understanding of the world.
Orochimaru's character would likely become more complex. He might start to question his past actions if he sees the consequences they had in the future. For example, if he travels back to a time when he was just starting his unethical experiments, he could see how those actions led to the destruction or harm of certain things in the future, and this could make him more hesitant or even try to change his ways. Also, if he meets important people from his past in a new light during time travel, like his old mentors or comrades, his view of relationships might change.
Eleven could be a likely candidate. Given her powerful psychic abilities, she might accidentally or purposefully time travel. Her powers have always been a bit unpredictable, and time travel could be an extension of that. She has a strong connection to the Upside Down, so she might be sent back in time to learn more about its origin or how to stop it.
Daenerys Targaryen. She has a strong will and a mission to claim the Iron Throne. If she time - traveled, she could meet her ancestors and learn from their successes and failures. She could also try to prevent the downfall of her family in the past, which would have a huge impact on the present state of Westeros in the fanfiction world.
I think Izuku Midoriya would be really interesting. He's the main character and has so much knowledge about the heroes and villains. If he time - travels, he could use his understanding of quirks and combat strategies to change the past or future in significant ways. For example, he could go back and give advice to All Might when he was younger, which might change how All Might deals with villains later on.
Ahsoka Tano would be a great choice. She has a complex history within the Clone Wars. If she were to travel back in time, she could interact with her younger self. She might be able to pass on wisdom she gained from her later experiences, like how to better handle the politics within the Jedi Order and the Galactic Republic.
If Anakin time travels, his character could become more self - aware. He might see the mistakes he made in his original timeline and become more cautious. For example, if he travels back to a time before his relationship with Padmé started, he could handle his emotions better and not let his fear of losing her drive him to the dark side.
A time travel scenario where a character goes back to the very first Hunger Games and tries to stop the whole concept from starting would be extremely dramatic. They would have to face the founders of the Games, deal with different social and political landscapes, and try to convince people that the future of Panem depends on not having these cruel games. It would be a battle not just of physical strength but also of ideas.