Why does Orochimaru's Laboratory have this item to hand? During episode 22, we see a test between Sarada's DNA and Karin's preserved umbilical cord. I can understand Orochimaru being the type of person to keep DNA on all his staff, but is there any symbolism, cultural significance or plot reason why in particular an umbilical cord?
I don't think there is, my guess is that it's just a real life reference to the medical field where umbilical cords are kept, as they have stem cells that are helpful to treat some conditions.

Those cells can differentiate into different types of cells, which would give some scientific base to some actions he has done, as injecting Hashirama's cells.