i have some experance of doing just this.
in addition in a tesla type system, you are charging capactors and therefore storing energy, so alough the neon transformers are current limated and (relatively) safe, the charged caps are deffanatly NOT safe.
it is quite possable to make a functional HF start this way, but unless cairfully tuned and tweeked, you will not be able to weld with AC, as the HF arc needs to occor at the right time in the AC cycle to re start the arc after the voltage swings through 0v
don't expect to get any increase in voltage from the HF coupeling transformer. regardless of the turns ratio between the coil the capactor is shorted through and the coil in the welding current path, you will get out about as many volts as you put in, so you want at least a 7Kv supply.
microwave oven transformers are LETHAL. they produce about 2Kv at about 1A, yes, 1amp, thats 2Kw, which there is no comeing back from if it gets in your innards.
Oliver