I recommend this plugin all of the time even though I have no association whatsoever with the plugin or the author of it. It’s free and allows you to add custom upload fields and all kinds of goodies to your edit screens without touching code. It’s called Advanced Custom Fields. Some developers would frown upon suggesting a plugin instead of writing something yourself, but seriously why reinvent the wheel when there is a free solution already?
That plugin will do what you want and make it a hell of a lot easier for you and the client in the long run.