NASA at least gets to pick which shuttle, if they have to go through with this. Enterprise, which is stored in a tent near the Intrepid aircraft carrier in New York, might be an option. There's no historical relationship between Intrepid and the Space Shuttle. Enterprise was placed where it is now by lifting it from a barge with a large crane. So it could be put onto a barge again and moved to Houston by water.[1]

[1] https://intrepidmuseum.org/exhibitions/permanent-exhibitions...