Well, this is an interesting question. I'd rather take my husband with me, but he is not a tool... I am pretty bad at fuel, so my choice will be a big knife. I think that it can help in self-defense, cooking, hunting, cutting wood, or making a shelter. I believe that it is warm on all islands, so I do not need the fuel much.
I can use the knife to take my life if I will be terribly wounded. Oh, but what am I talking about? I know myself, I would die because of fear or some infection in 15 seconds after realizing that I am alone on an island.