Can you still play WoW on an external hard drive?
Yes it will be possible to do this, the easiest way to do it would be to simply (re)install World of Warcraft making sure to opt for the "advanced" option rather than typical install. This will let you pick an install directory.
At that point you will be able to browse to the external hard drive and create a new folder called "WoW" and install!
I run all of my steam games from an external SSD, it is quite possible to achieve.