Yes, TPIC6C595 for sure.
Take a look at this schematic which uses a similar TPIC6B595 (can sink more current).
You'll need current limit resistors for each segment, approximately (10V - 2.2)/.03A = 270 ohms.
30mA may be really bright, you may want to consider higher value resistors to tone the display down some, like 10-15mA.
