In my world, a small population on an isolated island were bitten by radioactive electric eels while fishing. I read that the eels can send out carefully timed signals through their nervous systems to activate the electric organs which generates electricity . Science is still debating why they don't accidentally shock themselves. I'd like my subjects to be able to grow similar organs inside their bodies but with a safety mechanism in place (this is unprecedented because nature kept it a secret).
First of all, most of my reading on electric eels indicates that they do sometimes shock themselves, but that the real danger they face is the charge going through their heart. They have the ability to kill themselves with their own shock, but tend to shape themselves in a way that protects themselves as much as possible before discharge. But, for the purposes of the question, what mechanisms could humans use?
Humans have a distinct advantage over eels in this regard because they naturally live in the atmosphere, not water. Water is a great conductor; air, not so much. So, the real danger of humans having electrical generation organs in their bodies would relate to their capacity to touch their target.
In such a case, you're probably going to have some conduit that allows the electricity to flow through a given channel from that organ through to (say) the tips of their fingers. But, the human body is around 70% water which is a great conductor! What ever shall we do?
Fortunately, nature already has a solution to this - Cellulose. There are even electrical insulation papers that are made specifically because they are pure cellulose, and act as an insulator. This is a natural organic compound, critical in many respects to both plant and animal life, so your augmented humans probably have a tertiary circulatory system, made exclusively of some of hollow cellulose, channeling a conductive fluid (could even double up on the lymphatic system) that allows the discharge to release through the dermal layer.
In its present form, there are a LOT of problems with this model, but fundamentally in an atmospheric environment rather than an aquatic environment, the key to biological electrical discharges is going to be insulation that allows the electricity to be discharged to a contact point. If you have a need for a natural insulator, one that already exists in a biological context and is therefore not so exotic, cellulose would seem to be a good fit.
From there, the question is the design of the dispersal or circulatory system that fits into the human body to make all this possible in a similar manner to an eel.