Why is Sulu using a Rapier and not a Katana?
Cause he was gay.
Funny you should ask this question. I just found out the answer to it the other day while watching a video about Trek trivia.
Roddenberry had told Takei he could use either a Rapier or a Katana, and Roddenberry recommended he use the Katana.
Takei said that he would have liked to utilize the sword that was culturally appropriate for his character, but he felt that as the show was portraying the future in which people were no longer constrained by cultural pressures, he thought this idea would be better represented by choosing the rapier.
He chose to use the rapier because he thought it better represented a future that had shed outdated notions of custom and culture.