It doesn’t even quite work in real life, because cards yo discard without playing them should remain wild. It’s intended for playing using neither cards nor hidden board state tracking so that it can be played anywhere as long as you can access card text (e.g. from the PDFs).
If you want to replicate it in live play, the closest things seems to be that all known cards go to discard face-up, unknown cards face down, and techs remain besides your discard pile. You can exchange cards from hand to deck to (facedown, non-sideways) discard at all times.
This allows cheating a bit, if you (e,g,) draw four from draw pile followed by shuffling and draw one more, there is nothing here to track that you don’t swap two cards for stuff that couldn’t have been in your draw pile yet.
Letting players select drawn cards is not the same game as mental Codex, but it might still be a good variant for learning what’s possible.
As a side note on mental Codex: if the opponent gets to look at your deck, it’s going to get ugly.