It isn't really necessary to reinstall at all. You can just copy your installed operating system onto the other disk and boot it. If the two disks are of equal size, then it's very easy:
sudo dd if=/dev/disk1 of=/dev/disk2
This will make disk2 a clone of disk1, meaning that the partitions and everything will be copied. When the copy is finished, you can boot from the external disk, and have everything you had.
If your computer supports hardware virtualization, then you can also install kvm -- probably with virt-manager as a GUI -- and use the external disk as a disk for a virtual machine.