This is not currently possible through Steam, and there are no third-party tools either, but [I believe] it could be done because it seems that the data about whether or not an app has a third-party key is stored in part of the Steam client configuration (along with almost everything else Steam knows about each app). That part of the data is not easily accessible though as it is not stored in an easily-human-readable format (it's a special binary format of Valve's own making), but there are still at least a couple parsers out there that can manage it [namely built with NodeJS].
If you're still interested in this I could probably have something within a few days -- just about to go on a camping trip, so will be away from PC for at least two. An app would be able to automate the process to the point where what keys it can't find it would be able to list the names of so that you could then try to launch those through Steam to get the key(s). Could also give the ability to launch the apps of course, but that would kinda be overkill although it wouldn't take much to add it.