How to Separate 7 segment power supply
You should be just fine if you power the shift registers separately from the micro. Be sure that the grounds are tied together and that both power voltages are similar. 

You can run the shift registers at a voltage higher than the micro but not the other way around. In other words, the micro could be running at 3.3V while the shift registers are running at 5V. 

Just be sure that you are using the "HCT" version of the chip. Eg. 74HCT595