200 LED through arduino via SN74HC595N shift register
As far as I understand you want to control two strips of LEDs where each strip has 100 LED and you want to control each individual LED in each strip. So really what you want to know is how to do it with one strip - then just copy the circuit again for another strip. I'll explain how its done by building your own LED strip. 
You need to connect the enough 74hc595 chips together in "daisy chain" configuration- to make up as many outputs as you require (100 in your case). The you need to connect the "daisy chain" to a MCU. The MCU will actually make the patterns you require-by sending the pattern to the "daisy chain" circuit , and the 74hc595  "daisy chain" circuit just expands the output of the MCU. You will need to connect an LED to each of the 100 outputs to build your LED strip.
 You will need suitable power supply to light so many LEDs too. 
Personally I think charlieplexing by hand will be too tedious to do for so many LEDs.