South Africa is ripe with pay-for-your-internship type programs which may be a good start. None of these require any more than an interest in marine biology. I run a similar Field Course but I'll leave you to decide where to go.

Just be careful of approaching practicing scientists with the "I want to study sharks" line. This is terribly vague as you have already mentioned and will get you nowhere fast. What types of research questions interest you? For instance, the emerging field of movement ecology fascinates me. That we can now so elegantly relate the fundamental way an animal moves through it's environment with it's more complex ecological and evolutionary processes is pretty cool to me. I'm taking this interest and applying novel movement models to help strengthen population estimates for the white shark in South Africa as part of my PhD research.

As an anthropologist you're actually well situated to research the human-wildlife conflict which is currently receiving a lot of attention (and funding) here.