Moving from chemistry to oceanography as a current chemistry PhD student?
Chemistry and oceanography are quite closely related, with a lot of people who explicitly overlap the two.  A nice example that I happen to be familiar with is Chris Reddy at Woods Hole, who works on marine chemistry, especially in the area of oil spills.  There are lots more like him, so I think that a transition via postdoc is entirely feasible to attempt.

Whether you stay in biochemistry or shift to oceanography, however, I think that you may wish to consider the broader scientific ecosystem of research opportunities.  Your view of the biochemistry world is probably somewhat distorted by an environment dominated by highly competitive "big PIs" with large labs.  There's a lot more to the research world than that, even in medical biochemistry.