Fishy Calculation

Aaron Santos over at A Diary of Numbers, author of How Many Licks?, has posted a Fermi Contest.

For the uninitiated, a Fermi Problem is a seemingly unanswerable problem, which you can actually estimate reasonable by breaking the problem down into smaller parts. They're really fun, and I intend to post more in the future.

The question at hand is: How far would the oceans sink if we took all the fish out?

I'll answer in two very different ways.