Macs can boot an external USB fob.
Super easy. Get any respectable USB "fob" and format it in Disk Utility. Then run the OS installer and tell it to install on the USB fob.
When it comes time in the installation to reboot the Mac, hold down "option" to tell it. you want to pick the boot volume. Pick the external USB fob that you just installed the OS on. Now you will boot off that.
Now run Software Update and patch to the latest patch level for that version of the OS. (you can even upgrade to more modern OS if your hardware supports it).
Dismount your other boot volumes so they aren't corrupted
There is one wrinkle: your internal/main hard drive or SSD will now be visible as an auxiliary drive. That can sometimes cause complications with applications; for instance iTunes and Photos will go on a grand "fishing expedition" looking for iTunes libraries and Photos/iPhoto libraries on non-boot drives, will find your main drive's libraries, and corrupt them.
You can make sure that never happens by following the steps given in the next section to establish an fstab to automatically dismount every boot volume but this one. Now when you boot your external fob, your internal hard drive will NOT be mounted and will not be visible. You can "bring it back" manually by launching Disk Utility and mounting it.
All my boot volumes have the same exact fstab, which dismounts all my boot volumes. (the active volume fails to dismount itself).
The text below was authored by by user etresoft at Apple Community. The suggestion offered by user hyphen was incorporated into the text.
Sometimes, it can be useful to prevent a given volume from mounting at boot. You might want to hide an old OS version from Spotlight corruption. You just might not want to clutter your desktop.
Note: Encrypted disks are unlocked before the fstab file is read. In order for this procedure to work with an encrypted disk, you must first mount the disk, unlock it, and save the password in your keychain.
To do this, you will need basic understand of how to enter Terminal commands and use vi.
Make sure the disk you want to prevent mounting at boot is mounted.
Launch Terminal.
Run the following command to print out information about the disk:
diskutil info /Volumes/<volume that shouldn't be mounted>
Locate the line that starts with: Volume UUID:. Select the UUID (Universal Unique Identifier) that follows on the rest of the line. It will be something that looks like FF9DBDC4-F77F-3F72-A6C2-26676F39B7CE. Your value will be different
Copy the UUID to the clipboard.
Navigate to /etc by typing the following and pressing enter:
cd /etc
Edit (or create) an fstab file by typing the following and pressing enter:
sudo vifs
Enter the following line, substituting the UUID you copied in step 5. (Note: vifs uses the value of the EDITOR environment variable to pick the text editor to use. This article assumes you are using the default value of vim.) In vim, the editor starts in command mode. To add a new line, use the arrow keys to move to the end of the document and press the o key to append a new line and enter edit mode. Then type the following:
UUID=FF9DBDC4-F77F-3F72-A6C2-26676F39B7CE none apfs rw,noauto
and press the return key.
Type escape to return to command mode and then type ZZ (shift key down) to save and exit vifs (or some other method to save and exit if you are using something other than vim).
Type the following and press enter to reset the auto mounter:
sudo automount -vc
Quit Terminal
Now, the next time you restart, or unplug the drive in the case of an external drive, that volume will not be mounted. All you have to do is launch Disk Utility, select the grey, disabled volume, and click the Mount button.
You should be able to use a different text editor than vifs if you want. It needs to be able to edit and save files owned by root.
Note: If all of your disks are encrypted, there is an easier method. For any disk that you don't want to automatically mount, simply don't save the password to the keychain.
