Is it still possible to put the whole WoW folder on an external hard drive an just execute the .exe file (on the external drive itself) since the Blizzard Launcher came out (where all games are started from)? Or will it force me to first install/download the Blizzard Launcher on the computer?
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.