python - How to populate Unique ID field after sorting?

I am trying to create an new unique id field in a feature class. I already have one field called "SITE_ID_FD", but it is historical. The format of the unique value in that field isn't what our current format is, so I am creating a new field with the new format.

Old Format = M001, M002, K003, K004, S005, M006, etc

New format = 12001, 12002, 12003, 12004, 12005, 12006, etc

I wrote the following script:

fc = r"Z:\test.gdb\testfc"

x = 12001

cursor = arcpy.UpdateCursor(fc)



for row in cursor:
    row.setValue("SITE_ID", x)
    cursor.updateRow(row)
    x+= 1

This works fine, but it populates the new id field based on the default sorting of objectID. I need to sort 2 fields first and then populate the new id field based on that sorting (I want to sort by a field called 'SITE' and then by the old id field "SITE_ID_FD")

I tried running the script from the python window in ArcMap after manually sorting the 2 fields in hopes that the python would honor the sort, but it doesn't. I'm not sure how to do this in python. Can anyone suggest a method?