Slayer Exciter Health Hazards
Any time-varying current produces, in theory, a variable electromagnetic field (EM field). Whether or not this field will give rise to substantial EM radiation, i.e. EM waves propagating through space, heavily depends on various parameters of the source and its coupling to (i.e. interaction with) the nearby space.

Anyway, the more abrupt is the change of the current, the higher is the frequency of (the highest frequency component of) the EM field and the higher is the chance that whatever is connected to the source will act as an antenna, giving rise to substantial EM radiation.

An electric arc, such as yours, is a very complicated beast, from an EM point of view. Not only it is a powerful pulse of current (hence very rapidly varying from 0 amps to its max), but it breaks through air, ionizing it in the process.

From an electric safety standpoint an electric arc may be dangerous in itself: it may escape its intended trajectory (like a small lightning), and make flammable things catch fire. Even if it lands on things that are not flammable, e.g. metal surfaces, the ionized air it produces, which is highly conductive, might cause short circuits in other parts of nearby electrical systems (maybe producing other arcs!). This may lead, in unfortunate circumstances, to a cascade of other failures in nearby circuits and systems, which may have dangerous consequences.

Now let's get to the EM wave part. 

As I said, a rapidly varying current pulse will generate a corresponding EM pulse (EMP), i.e. a short burst of EM waves propagating from the source, which will cover a very broad part of the spectrum. How wide is the part of the spectrum that will be covered (and how powerful the EMP will be) is not easily calculated, given the complexity of the phenomenon. Small sparks may disturb radio communication well into the hundreds of MHz range (ever heard short cracks in your FM radio receiver when you switched a light off? That was the EM pulse of the small electric arc that forms in the switch during switching.)

Another thing to consider is the power associated with the EMP, which depends on the entity of the current variation. A 1mA-carrying spark will deliver a much feeble pulse than a huge 10A arc produced by an electric welder!

The problem with EMPs, especially powerful ones, is that it is difficult to shield a circuit from them, because they are so broadband. Even a Faraday cage is not going to suffice, unless it is a completely closed box of highly conducting material (even a single small hole in the "cage" can let some radiated energy inside, if you are unlucky). And even if the cage were a completely closed box, sufficiently powerful EMPs could "force" some EM radiation inside (only if the box material were ideal, perfect conductor, this wouldn't happen, but that's theoretical). That's why even armored tanks must be tested against EM pulses from, say, a possible nuclear blast.

If the pulse is powerful enough, even a small fraction of its spectrum will have enough energy to damage sensible circuits if they are not shielded or protected from signals at those frequencies. Any little piece of metal (or conducting surface) inside a circuit could act as an antenna for that tiny part of the spectrum that happens to bypass the shielding of your equipment. Once captured by that "antenna", the EMP will induce currents (and voltages) in the circuit it has broken into. If the power of the EMP is big enough, the induced currents/voltages will be able to destroy something (or everything) in the device!

EDIT (To address a comment by the OP)


  ...if metal nearby can act as an antenna, our nerves can too or is that due to the skin effect caused by the frequency?


Efficient antennas need to be made from high-conductivity materials and/or must resonate with the frequencies they are intended to receive. The human body is not so good a conductor, after all. The EMP can interact with human body structures and part of its power will be dissipated inside it, hence causing a very little temperature rise (unless we are talking about EMPs generated by nuclear weapons, but in that case there are greater dangers for people other than the EMP). 

Small arcs, even if rather powerful from an electric circuit POV, cannot radiate so much power as to endanger a human by simple temperature increase (remember the EMPs are short in time, and the energy transferred in that time is limited).

The direct interaction with human nerves is debatable. Human nerves don't work as metal wires, as someone believes. The conduction of the nervous impulses through the nervous system is electrochemical, thus a nerve is not going to resonate with the incoming EMP as a trace on a PCB might do. Therefore significant energy transfer between the pulse and the nervous system is unlikely, at least when talking about EMPs generated by arcs that have a relatively low power level.