I wouldn't fly through any thunderstorms, but here are my notes for flying around oceanic thunderstorms:
Oceanic thunderstorms (barotropic, meaning the storms formed in a front-less region of uniform temperature) tend to have less mass and significantly less reflectivity than continental thunderstorms (baroclinic, meaning storms formed from distinct air masses of colder and warmer air) of equivalent height.
The reduced mass and lower reflectivity levels found in oceanic thunderstorms occur due to the fact that they have, on average, less water content than do thunderstorms that form over land. As a result, a higher gain setting and/or a lower tilt setting may be required to adequately detect thunderstorm threats at higher cruise altitudes.
It is not unusual for oceanic thunderstorms to be very “skinny” but still have significant vertical development, especially in equatorial regions. This type of thunderstorm has very little moisture content and is extremely difficult for radar to see.
Oceanic storms do not generate hail in large quantities or large sizes because hail can only be generated by strong updrafts (convection), which is produced by large temperature differences in the air mass. Hail forms in vigorous convective clouds that have high water content.
Over land, solar heating produces a rapid change in temperature of the land, which is then imparted into the air near these hot surfaces. These large temperature changes produce convection currents that can drive large quantities of moisture aloft. In order for hail to be produced, these convection must persist for a significant period of time and over large spatial regions.
Over the ocean, solar heating only slightly heats the water and the air above it, resulting in the production of only minor convection currents which are insufficient to sustain hail formation.
Additionally, land surfaces (and the air associated with them) heat unevenly and thereby produce uneven air currents that contain large shears (variation wind speed and direction) in both horizontal and vertical directions and over both large and small scales; whereas, oceanic surfaces (and the air associated with them) are more uniformly heated and thus only have minor shears within them.
These shear conditions are required for hail production (methodology that allows for multiple layers of ice and increases in particle mass/size (and thus an increased hazard to aviation)). So typically, oceanic storms do not have the meteorological properties required for hail production. In completeness, some oceanic storms become large enough (eg, hurricanes) to exhibit strong convection and enough shear for small hail production but these conditions are severe enough that the radar reflectivities in these regions are huge and thus the hail conditions are easily avoided by pilots simply on the basis of radar reflectivity alone.
Storms that develop out over the water establish their meteorological characteristics from these conditions; once they begin to go over land they slowly begin to take on more continental characteristics but that takes many hours or even days for these storms to morph into continental storms. Most storms die out prior to changing their characteristics and then new storms form from the atmospheric instability that initiated the original storm; so for the most part, storms that develop over the ocean retain these characteristics throughout their brief life time and once they go ashore they die out and other storm cells/complexes that may show continental characteristics will take their place.