Driving two large 7-segment displays using Arduino and shift registers
They are common-anode, so charlieplexing is out. 
Multiplexing does not reduce power consumption, it only (may) simplify the drivers. You only have two displays, so you may as well not bother and drive them statically. The ratio of peak to maximum current is very low on these displays (only 1.5:1 for 10% duty cycle). 
There are two parallel strings of 6 series LEDs for each segment, as shown the the datasheet. The decimal point has one fewer and apparently a resistor (not as shown). The voltage is for all LEDs in series. Since that voltage is around 12V you should use a higher voltage supply such as 15V or maybe a 19V laptop adapter. 
You can use 2x ULN2003A drivers along with the 2x 74HC595s and 14 resistors to control the displays. The ULN2003A drivers will drop around 0.8V at 15mA, so you can find the resistors as around 150 ohms with a 15V supply or about 430 ohms with a 19V supply. If you use the decimal point be prepared to change its resistor value to match the brightness, and you'll also want to use the ULN2803A which has 8 drivers per chip rather than 7.  
20mA is the absolute maximum current at 25°C so don't attempt to run them at that current unless they are going to live in a refrigerator.