Many of the basic oceanographer duties are carried out in an office-type setting—conducting research, writing proposals, or publishing findings in journals. Not a ton of danger here, unless you don't know the proper way to operate a stapler.
Other aspects of the job might pose some physical danger. Laboratory work can expose oceanographers to harsh chemicals, heat, or sharp instruments. Equipment can fail without warning, like when a saltwater sediment test tank gets over-pressurized and a cascade of ocean muck takes you down.
Field work can be the most dangerous of all. Being on the open ocean for any length of time is an unpredictable scenario, and oceanographers need to be prepared for the unforeseen events which can take place at sea: rogue waves, sinking ships, hurricanes, and shark-infested waters.
Luckily scurvy is a thing of the past. Just remember to eat your oranges.