I would seriously consider installing Steam itself onto an internal disk, and then creating a library folder on the external disk (and setting it as the default). This would avoid any weirdness by having the Steam app inaccessible when the external disk is not attached. Only the games on the disk become inaccessible when removed (which should be the bulk of the disk usage)
I have a tablet PC, which doesn't have enough storage on the local/internal 'disk' to be able to install (most) games on. Instead I have a steam library folder set up on a micro SD card, to which I install any games I play on it.
Sometimes I need to put a different SD card in there - the games on the SD card just become unavailable, but as soon as I put the steam one back in they appear as installed again.
This also happened when an SSD disk in my PC 'dissapeared' due to a BIOS glitch.