The problem with updating the back up is that its data may not be 100% up to date if a user has made changes since that back up was made. So I would download a copy of the live file using the Admin console.
You can then remove the live copy and use filemaker to upload the updated copy to take its place.
This kind of update really needs a planned outage for your client.
Assuming you have all the changes tested on your development server, if you are just adding layouts and scripts it should be pretty quick. Make a checklist of all the things you need to update before starting to minimize downtime and errors.
Download a copy of the closed live file directly from the admin console. Do not use a backup.