Electric fish don't fry themselves because their discharge lasts no longer than three milliseconds. Source for the pulse duration: section III of this article about using electric eels to power lamps, because science! Seriously. Those guys even put this nice little graph about what they intend to do, I don't now why they didn't get the IgNobel in 2014:
Anyway, back to the topic at hand. Eels also don't fry themselves to death because while the voltage is high, the amperage is very low (for the eels). Prey gets stunned (or forced to move) because it is much smaller than the eels. It's like applying 45v to an adult man with gigantism and a toddler: one of them will shrug it off, the other will be quite jolted.
In eels the electrocytes are stacked along the length and the voltage is proportional to the length of the stack. Therefore, due to the Square-Cube law:
- Voltage scales linearly with length;
- But amperage will scale by the power of thirty two (25). $I=VenA$, where $I$ is the amperage, $V$ is voltage and $A$ is cross-section area. $e$ is the electron charge in Coulombs and $n$ is the amount of free electrons. Only the electron charge is constant here. Area scales quadratically and the amount of free electrons scales cubically.
Since the strength of the current grows so much faster than the body mass, at some point not far from the biggest size electric eels can attain in real life (~2.5m / 8ft) the animal starts frying its own nervous system when or discharges. A whale sized electric eel would be able to discharge exactly once in its life; it would form a few bubbles around itself from vaporized skin and innards escaping its body, but nothing impressive. It would then lifelessly sink to the bottom of the ocean.
Now, about this:
The idea is a species of Electric eel that swims in the open ocean.
Someone once asked Randall Munroe (the author of XKCD) about the feasibility to electrofish for whales. He had this to say:
So you want to give endangered whales powerful electric shocks. Great! I'm happy to help. This is definitely a very normal thing to want to do.
But he also said this:
(...) there's a catch: Most electrofishing is done in fresh water. Unfortunately, blue whales live in the ocean, where the salt water conducts electricity much more easily. That might seem like good news for our electrofishing plans, but it turns out to make it much more challenging.
Electrofishing works best when the water and the target animals are about equally conductive. In highly conductive saltwater, most of the current flows past the animals in the water rather than through them. This means that ocean electrofishing requires much more power.
In the article Munroe mentions that in order to shock a whale in the sea you'd need three orders of magnitude more power than if the whale were in a river. Your mega-eel's sacrifice might just do it, or it might turn a whole school of fish into unedible coal-like stuff. But in any way this is indicative that fish would have little evolutive pressure to evolve gigantic electric organs in the open seas.
If you want a natural, impressive weapon for underwater, consider what nature has already provided. There is poison, suckers with hooks, animals that swallow prey larger than them etc. I am personally terrified of the portuguese man'o'war, which can have venomous tentacles as long as 50m / 165ft!