If you're afraid of the water, this may end up being fairly stressful for you. Same goes for fear of boats, sharks, storms, fish, maps, and geometrical calculations. If you're okay with those things, then you've already passed the first hurdle.
Whether conducting research or calculating data, oceanographers need to show results. They're scientists; they need to be able to process a huge amount of information and observations about marine systems and turn them into viable conclusions. To get that data, they may need to travel to remote corners of the world, navigating physical challenges and foreign nations, and maybe even running from pirates (not as fun as you might imagine).
So there can be stress, especially if you don't enjoy waiting in long lines or wading through red tape or filling out forms. But we're talking stress in the name of science, so it ain't all that bad.