Are you familiar with installing things on an external drive? While I'm not well-versed with macs despite ironically typing this on an imac (bootcamp though), you'll need to declare the location of the external drive during the installation process. AFAIK with mac installers, it's a bit different where you have no real immediate choice. I can't confirm this process since I don't have OSX installed anymore but here are instructions from stack exchange.

https://apple.stackexchange.com/ques...installing-osx