I doubt that this is possible. With a Synology NAS, the DSM (DiskStationManager) operating system is installed on the hard disks. It will be similar with the QNAP NAS. I think it is unlikely that the Synology NAS will boot without errors with the QNAP operating system.
The best thing to do is to use a SATA2USB adapter to back up the hard disk data to another drive. (Instructions for this are available on the net). Then reinstall the new NAS with the old disks and restore the backup. Alternatively, ask the manufacturer if you can buy the power supply separately as a spare part.