Not sure if your laptop can play this mini-sized DVD, but assuming it can, you really dont need FCP for this, if you have DVDSP.
Copy the VIDEO_TS folders from both discs onto your hard drive.
Use MPEG Streamclip (available free) to demultiplex the relevant video files. Assemble them onto a video track (or tracks) in DVDSP and create a new DVD.
You should have your client assume the risk for repair, if this mini-sized disc gets stuck in your computer.
MPEG Streamclip available here: https://www.squared5.com/