74HC595 Rows/Columns to drive LED matrix
You can do it the way you suggest, however you should move the resistors to the NPN collectors, and you will need PNP (or emitter-follower NPN) transistors on each row output. 

To get a rough idea of the current required- if 5mA is enough for the LED to be bright enough when supplied with DC you will have to supply 20mA for 1:4 multiplexing, and each row driver will have to source 80mA with a 25% duty cycle. Each column driver will have to sink 20mA with 100% duty cycle.