First make sure you have a backup. If something goes wrong you can loose your data.
It should work, but you don't need to build a RAID1 (mirror) array. This would take 12-24 hours.
Leave the disks independent, the firmware partition is mirrored anyway even if the data partition is not.
What I don't know is if the working CS will give an error after removing the disk, and if you will be able to get rid of the error.
After installing the new disk in the diskless CS, be aware that you have to change the network name of the CS. If not, you will have duplicate network names.