The original circuit used an audio transformer that works perfectly at the fairly high frequency used. Your low frequency mains transformer might not work at the high frequency. The slow mains diodes also might not work at the high frequency.
The simple circuit might stun a mosquito, not a person.
The original 8 ohms to 1k ohms transformer steps up the voltage about 67 times. Your 9V to 220V low frequency transformer will stepup the voltage a little more than 25 times.