She may also collect Shiryu's nodachi, whoever beats him.
I consider that a real possibility. Tashigi has yet to confront someone evil wielding a Meito. And given her and her squad are becoming buddy-buddy with the Strawhats, the likelier it is she confronts Shiryu, who is the definition of the bloodthirsty killers she detests.
She may get it, Wado and Zoro's main sword
I don't think she will claim Shusui. That is Wano's national treasure, wielded by a legendary hero of the country.
Remember, Tashigi does not want to take swords from good owners.
Though Zoro might willingly offer her Wado Ichimonji once he accomplishes his dream. I don't see Tashigi asking for it herself since I believe she'll deem Zoro a good person at that point.