People forget that suigestu said, " I thought this if from when karin was born but ", this means he not 100% sure this is karin's cord. He is assuming that it is because it is in karin's desk.
This opens up the possibility of it being sarada's because we know that sarada was born outside of konoha and both sakura and sasuke were not present in konoha (naruto's conversation with suigestu suggests this). Get ready for sarada to go ape sh*t on sasuke, and for sarada and us the readers to finally get answers from sasuke of the origins of sarada birth.
This assumption could all change depending on the viz translation.