A script or model makes sense, but there is another way you could do it...
Export to Cad allows you to have multiple inputs, that is, multiple shape files at one time.
Also, if you have a field in your source shapefile that specifies the output path (DOC_PATH) of the cad file, Export to Cad will output to that file instead of the one specified as the tool parameter.
So...if you added and populated the DOC_PATH field, you could add all the shapefiles as your input and execute the tool once.