So I need ~1MHz @ ~10amps into <1ohm

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The power supply is probably current limited, look at the specification.

It might even be limited to such a low value that it's impossible to recieve a lethal shock from it but don't take my word for it, I could be wrong.

You couls also loot at how long it takes to charge the capacitor to the spark over voltage and calculate the current from the capacitance equation.

El zappo...

If it's current limited then the capacitor won't be an issue. You could put a 1000:mu:F capacitor on the output and no harm would be done. Ignoring leakage, it would take 10000 seconds to charge to 10kV.

1mA isn't enough to kill you but you'll certainly feel it and a charging a capacitor is dangerous as the stored energy can kill you but it depends on how much energy you have. 1nF@10kV is 10mJ and will give you quite a nasty shock, be careful!

The welders works with similar devices (arc striking devices from welding equipments), they are not dangerous.
The international standard IEC 60974-3 specifies safety requirements for arc striking and arc stabilizing devices used in arc welding and allied processes (typically plasma arc cutting and arc spraying).
High-frecquency - High voltage generators is applicated to automatic TIG welding (old equipments).
The TIG AC welding of aluminium is not posible without a stabilizing device based on High-frecquency - High voltage.
When high frecquency is used, certain precautions are required to prevent interference with communications equipment.

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Sorry 50mJ, it's 0.5CV², I don't know what I was thinking.

I've come to refer to those as 'brain farts'. It's a good thing they don't smell, my coworkers would complain about me