I would let her opt out.
Responsibility only develops if the challenge is manageable. If wearing the armband makes her anxious enough that it spoils the game, repeatedly forcing it is unlikely to teach the lesson the coach wants.
You can still give her small leadership experiences that suit her better: choose the team name for a training game, help a new player, lead a two-person warm-up, or simply be the teammate who welcomes someone.
Then, if she becomes curious about captaincy later, the door is open.
I would also make sure opting out is treated as normal, not announced as “she doesn’t want to be captain”.
Different children show leadership differently.
At U9, confidence is not built by making every child perform the same public role. It is built by stretching them gradually from where they actually are.
