Ubuntu server live usb
Solution 1:
We are creating a live server for 18.04 LTS that will enable simpler installation in the common cases, but also be generally useful for everyday testing. See http://cdimage.ubuntu.com/ubuntu-server/daily-live/current/ for the current build, bugs and comments welcome.
Solution 2:
There is no true "Live" option on Server editions (they don't have a "Try Ubuntu" option in boot menu). I think they are built only with installations in mind.
Also usually most Linux default liveCD/DVD editions refer only to their desktop variants. See this answer.
To achieve your goal i'll suggest making the LiveCD from scartch (not starting from existing LiveCD) following the instructions you already linked.
To do this, you need a linux host (it's a base and inevitable requirement). If you can't install on a true PC, i'll suggest doing it inside a virtual machine (maybe with VirtualBox o you preferred hypervisor) to make the LiveCD iso from there.
Hope it helps.
UPDATE:
I discovered a simple wizard to create ubuntu ISOs it's called Cubic and maybe worths a try. More info.