I've been looking into this for a few days, so I can save you a step here.
Installing onto a USB drive is not the problem. You can get an installed copy there via other means, but it won't help you, because:
"Windows 7 will not boot from a USB drive."
That's the official word from microsoft. Ignoring them, I have gotten it to the point where it shows some fancy logos, but then BSOD.
Apparently it is possible to bypass that, by modifying some driver files, and installing a service to keep the modified.
But just to be clear, INSTALLATION is not going to be your main problem.