[SOLVED] Installing Ubuntu onto External HDD and booting onto Razer Stealth

Are you wanting to try to convert existing install to UEFI, or are willing to start from scratch.

Drive will need to be gpt partitioned. That erased drive, but gdisk or sgdisk can convert a drive. Either way really good backups are required.

Ubuntu's grub does not make it easy to install to a second drive. I have several installs on second inteal drives and exteal flash drives.
You have to partition in advance to be sure to have ESP on second drive. I typically include a bios_grub also just in case later I want to experiment with BIOS boot. I then add a 25GB / and use rest of flash drive as data partition.

But even if during Something Else you tell grub to install to sdb. And grub will say installing to sdb, it overwrites or installs to sda.

You then copy /EFI/ubuntu twice, once to /EFI/ubuntu on sdb's ESP and again to sdb into /EFI/Boot. In /EFI/boot you rename shimx64.efi to bootx64.efi.
UEFI only boots exteal drives in UEFI mode from /EFI/Boot/bootx64.efi. Both Ubuntu & Windows installers use that file name, even though different files. So that file has to exist on an exteal.

When we copy the grub or shim from a full install on sda, that version of grub is hard coded to find files in /EFI/ubuntu, so you must have both /EFI/ubuntu and /EFI/Boot/bootx64.efi.