A close friend of mine suggested this organization for cord blood donations. It is one that is very dear to her heart, as it saved her sister's life when diagnosed with Leukemia.
The only thing they do is take two extra vials of blood and they ask about your medical history. The kit is sent to you to give to the hospital with instructions on how to transfer. I hope this helps.
https://www.dukehealth.org/health_library/news/kit_based_cord_blood_program_gives_moms_new_options_for_donation