I'm also assuming there will be fresh water on the island. I'd take:

Elucence MBC
AO HSR Condish
Aloe Vera juice
Oyin Hairdew (Am in )
Castor Oil
Jojoba Oil

I really need to change the products in my siggy!
Products in current rotation:

Terressentials Pure Earth Mud Wash; Elucence MBC (now really just for cowashing, leg shaving or emergencies); Curl Junkie: Repair Me, Deep Fix, Curl Rehab; AOHSR (retiring); Oyin Handmade: Honey Hemp, Hair Dew, J&B; Qhemet Biologics: BRBC (retiring- prefer Oyin HD), AOHC, OHHB; Jojoba Oil for scalp; Castor Oil or Shea butter to seal; Henna & Ayurvedic pastes when I can be bothered.

Still searching for the perfect stylers, but loving CJ CIAB over everything so far