Shapefiles don't have any sort of symbology attached.
Since you're working with ESRI tools, why not wrap them in a layer package? Here's how.
From the link: "When users add a layer file to their maps, it will draw exactly as it was saved as long as they can get access to the data referenced by the layer."
Just be careful to use relative paths, and keep them the same. (The .lyr augments the shapefile; it doesn't replace it.)
Edit to add: you'll also be using the AddLayerFromFile method, rather than AddShapeFile.