Creating a normal Win10 system that runs from a USB(?)

[MartynA]

What I started off trying to do is to use a MacBook's Bootcamp to run Win10 on it.  There isn't room for Win10 on the MacBook's internal disk, so I've been trying to make a USB with a copy of Win10 on it.  I got nowhere with trying to use the BootCamp Assistant to do that, and a bit of googling got me to WinToUSB.  But I'm getting nowhere with that either, because:

I've created a Win10 ISO image and used the Windows Installation USB Creator to put the image onto a Lexar 128 Gb USB drive.

My normal Win10 PC will boot from the USB fine, and enters the Windows SetUp program.  Where I run into the sand is at the step where I'm supposed to choose a partition to install Win10 onto.  What I want to do, of course, is to install it to the USB itself, but that's the one disk that the drop-down list of available disks doesn't list.  I've no idea whether the USB would be listed if there was space for another partition on it, but the Win10 Disk Management utility says there's no free space on it.

So I'm beginning to wonder if it's even possible to install a runnable version of Win10 on a bootable USB drive.  So my first q is wherther that is possible or not and, if it is, my next question is how to do it, seeing as the Win10 SetUp program won't give the option of installing it on the USB?  

I hope that's all clear,

Thanks Martyn