Install windows on another HD through a caddy / USB

Hey,

I have Windows 7 on a new laptop I bought but I need to reinstall Vista on my last laptop.

I have a disk for each but the DVD player/recorder is broke on the Vista laptop, I was hoping I can install it through the new laptop.

I have a USB caddy that I connected to the new laptop to get my files from it and hoped I could do a fresh install of Vista through it.

I know it can be done through USB stick but I don't have 1 with 4gb which is needed.

Hopefully someone can help :)

Thanks!