Export to a Shapefile and maintain Domain Coded Values

I'm not sure which version of ArcGIS you are working with, or if you've come across this since posting, but in version 10.1 there is an environment setting under "Fields" called "Transfer Field Domain Descriptions". I've used it on occasion in the Feature Class to Feature Class tool to export to shapefile and it seems to do the trick (if you don't mind your output data having additional fields added for the descriptions).

In version 10.0 the same tool, Feature Class to Feature Class, apparently did it automatically (the last dot point under Usage). Not sure about earlier ArcGIS versions though.

1. Create lookup tables like @GeoKelvin discribed. Or use tool Domain To Table to create a lookup table.
2. Join lookup table to feature class
3. Export feature class to Shapefile

You can automate this with Modellbuilder.

You could create CSV files for your domain codes that can be distributed with the shapefiles. Using your example values, create SourceCode.csv to look like this:

SourceCode,Source
1,Integrated Registered Survey Plan
2,Survey Plan
3,Geo-Referenced Air Photography
4,Government Provided
5,Expert Knowledge
6,Unknown

If you distribute the CSV files along with your shapefiles, the recipient will be able to join the tables and get the meaning. This will prevent you from maintaining a separate copy of your spatial data for distribution, or from calculating the values every time you have to distribute the data (both assuming you don't keep the new attribute in the production data).