There's two ways to do this:
1. You would need to make it a two part application: a daemon to do all the actual work, and a frontend to interface with the user. The daemon would set the permissions to something unreadable by the rest of the users (I have no idea how you'd protect it from an admin account though, especially since they can sudo) as the files are created.
2. You would need to incorporate something like Pseudo directly into the program; whereas Pseudo (AFAICT) uses an NSTask to launch "sudo open -a /path/to/application.app", you would need to have it su to the separate, password protected user account that would be created on first run. There's still no way to protect it from an administrator however.
As for the rest of the program, I can't help you much, but good luck, and look into using WebCore, as opposed to just WebKit.
Oh, and incidentally, in my experience, Macromedia Contribute is absolutely terrible. Avoid if possible.