The suggestion to make your computer dual bootable, now with both an OS 10.9 partition and an OS 10.15 partition, probably won’t work, for two reasons. (Space on drive isn’t a reason, since you can install a larger one.) First, when you updated to 10.15 you likely updated your firmware too. The new firmware probably won’t allow your computer to run under 10.9, even from an external drive. Second, the update to 10.15 surely reformatted your hard drive to APFS. OS 10.9 can’t operate with that new file system.
I suggest you edit using FCP 6 (or 7) from an external drive, and with OS 10.12 (Sierra) rather than 10.9 (Mavericks) as the operating system. Put OS 10.12 onto a USB 3.0 (or Thunderbolt) external SSD and check if it can boot your computer. (Alternatively borrow one, or ask someone who knows Macs really well.) If it can, then install the old FCP 6 onto it. FCP 7 runs half decently under OS 10.12, so hopefully FCP 6 will too. If you are not terribly demanding, a USB 3.0 connection will let you edit happily with the old FCP.
If this works it’s no harder and much cheaper than setting up a new computer.
FCP 7 will open FCP 6 project files.