I think this is solved enough to finish. I wasn't quite able to use any ISO I wanted but I have a working "rescue partition" which is good enough.
Duzzy, the usb installer that you linked to would only allow me to select the entire hdd, and not just the partition I had set aside. I assumed that if I proceeded I would have formatted my backup partition too (on the same external hard disk).
So I then tried the universal usb installer that gregrocker suggested. First I tried selecting one of the last two options (old syslinux) and then chose a boot utility ISO I had already downloaded. Trying to boot this led to the first "SYSLINUX..." line showing up but then no further activity.
I tried again with the universal installer but choosing a supported option from the list (Trinity Rescue Disk) and this booted fine, so up and running with this. Thank you very much for your help, both of you.
DIRECTIONS for anyone trying to do this. It's pretty simple. Download the Universal USB Installer and follow the instructions.
To create a bootable rescue partition on an external hdd.
1. Create the partition of suitable size (5GB for example) on your external hdd. Use any method you like such as diskparted or diskmgmt.msc in Windows 7.
2. Download Universal USB Installer
3. Select one of the supported rescue disks of your choice and check the box to download it.
4. Browse to the downloaded file and check the "Show all drives" box.
5. Select the partition you previously created. MAKE SURE YOU HAVE CHOSEN THE CORRECT DRIVE.
6. Check the "Format drive" box and click create.