Use 2 USB drives and just install directly to the 2nd one.
I wouldn't recommend that tho since there are only so many writes a flash drive can take before it starts causing problems. Try a small distro that has the option to load everything to a ram disk. Then if you want a persistent save it'll just write all changes once back to the drive before it shuts down. I used a small SD card on my phone running like that, so I could put recovery stuff on it. Plus a couple of Winblows isos to fix my mates PCs. If its an external HDD you don't have that problem. Just run it as normal. If you are worried about installing grub to the wrong drive, just disconnect your internal HDD and use the external one as I it were the usual local drive.
I had also installed from a USB drive to a really old SD card on a laptop with no HDD at all as a backup backup. Lol it is slie as hell, but its handy to have about. Hope this is of some use.