Install an older version of MacOS onto an external drive without USB installer?
You don't need a USB stick, you can create a small partition on any existing drive &amp; createinstallmedia to that, then select it with an alt-boot. 

One thing you do not seem to be able to do is install a new OS to any other disk whilst there is a fully-bootable OS disk already present, it wants to 'update' the existing OS even if it's exactly the same OS.
You have to remove any current OS disk first, then it will ask you which to install to.

[Source of info - just spent the afternoon messing at this myself.]