You can write the GRUB boot information to the USB disk directly fro the GRUB shell, but can you boot from that disk at all? Before you do anything else, I'd recommend installing one of the USB booting mini-distros on it, like Feather Linux, to make sure your BIOS and disk support booting.
I have two apparently similar USB sticks, of the same make, one boots the other will not.
"Insanity: doing the same thing over and over again and expecting different results." (Albert Einstein)