I don't know what would happen if they wanted to register their exchanges in Seychelles but if they aren't falling under American regulation there shouldn't be a claim on their users trading data. If the biggest exchanges challenge the govt in court it's going to help the smallest exchanges stay in business.
I think that these exchanges are going to risk losing a part of their clients if that's what it takes to be able to transact in the country.
What choice do they really have? Give up users or shut down. They can also fight the government in court but that could take time and be expensive. Only the biggest exchanges will try this.