Looking for some help on this please.

http://www.kmitl.ac.th/~kswichit/Led/Led.html

Taking the LED segments from that schem, and use a PIC 16F627 to drive them as a clock.. what else would I need to change?

The 595's would be taken out, the ULN2003 would stay to drive the led segments.

I would need more outputs to control the Common Cathodes from the PIC, would I need to place a ULN2003 on those outputs as well?

 

If you are going to have multiple digits you need some way of enabling each digit. For this I would utilize a single P-channel FET on the annode. This would mean relocating the current limiting resistors to the cathode (just prior to the 2003) then tie all the lines together in a common anode configuration.