No, Hiawatha uses the extension to determine if a file is a CGI or not.
Maybe you can make the thing work with the ErrorHandler option. Create the directory you want to use as your 'interprets-every-file-below-a-certain-directory-as-CGI-scripts' directory. Place a .hiawatha file in it with the ErrorHandler option in it:
ErrorHandler = /errorhandler.cgi, 200
This errorhandler.cgi is a shellscript which will execute the right CGI based on the URL. Be sure to only handle 404 (File Not Found) errors. This errorcode can be found in the environment variable 'HTTP_GENERATED_ERROR'. This should do the trick.