Hi lucy,
I assume you are doing that as an experiment.
You won't be able to boot a Windows o/s from a usb attached drive. You should be able to store data and install programs on the external drive.
However, Windows needs more space to breathe than you have remaining on the 8gb drive.
You could remove some of the things you don't use from 7 , like speech support. tablet pc, accessibility - and numerous others.
You can do it with vlite - get v1.1.6 as it does not require The enormous WAIK download and can work as is. You can install v1.2 over the top of it.
Remove what you don't want from the 7 installation files - it will rebuild them and create a new .iso .
Then install that - should take up less disk space - could be a lot less depending how much stuff you take out.