Your approach looks good on screen, but it won't work for two reasons.
1. Except for *very* expensive high-end units, audio amplifiers do not have the bandwidth to pass signals up to 500KHz frequency. For that matter, neither does the output section of your sound card. The waveform might look square on the computer screen, but it won't on an oscilloscope. Square matters.
2. Except for expensive high-end units, audio amplifiers are not DC-coupled. They have components in them specifically to remove any "offset". Again, the sound card probably does the same thing, and again what is on the screen is not what's going out the door. For unknown reasons, offset matters.
Also, your approach is not safe, but I disagree with the ususal reasons. I have no problems with AC powered (as opposed to battery powered) devices being connected directly to the human body, given what it takes to get a power supply certified in this country. The problem in your case is the size of the power available. Between the small battery and the 1000 Ohm output resistance, typical Zapper designs are inherently limited to very low amounts of available energy. A 20 watt stereo has way more current available, even at low voltage settings. Not good. Current matters.