I think this link that may help: How do I install Ubuntu to a USB key? (without using Startup Disk Creator)
In short:
Install qemu-kvm package and dependencies if not yet done so.
sudo apt-get install qemu-kvm
Run virtual machine with external HDD (assume it is mounted at /dev/sdb) as internal drive and Ubuntu ISO file as cdrom. Add more ram to virtual machine with
-m 2GB
if you have plenty of ram on your machine to speed up installation process.sudo kvm /dev/sdb -cdrom ~/.cache/testdrive/iso/ubuntu_natty-desktop-i386.iso
Personally, I prefer to run any installer on target PC/laptop instead of remove HDD from it and install at another PC/laptop.