My intuition strongly says that shuffling one card counts as shuffling. That seems like it would make the Stash interaction simpler. Shuffling just means randomizing the order of all the cards in your deck. That there happens to be only one outcome is irrelevant. What if I and all other players know my deck consists only of Copper (more than one Copper). Do I not shuffle then because there is only one outcome? I think this is a natural extension of the reasoning that you would need if you wanted to conclude that shuffling one card is not shuffling.
This one is easy to refute. In Dominion all Copper is not created equal. I fear you are losing track of the fact that this is about lose-track.
The only card that can be kept track of in your deck is the card on top of your deck. It has absolutely no relevance if it has the same name as the rest of your cards in your deck. If you shuffle it in, it's lost track of. It was
that Copper, the one on top of your deck, that abilities kept track of. This is the essence: Did the card move? There's no way for it to move if it's physically impossible to shuffle it.
But really it's just about what feels right, and I'm skeptical that most people would disagree with me. It especially feels more natural with other Dominion rules to me, but I'm not sure why.
Maybe these two earlier rulings by Donald will help.
1) If you have Inn on top of your discard pile and screw around with the order of your discard pile while at the same time keeping Inn as the top card, Inn did not move and is not lost track of.
2) If an ability tells you to shuffle an already shuffled deck before any card is moved to your deck, you don't shuffle, because it's already shuffled.
Yeah I think Inn is key here. If "shuffling 1 card" were an impossible to follow instruction, then it could follow that if you gain Inn while your draw deck is empty, that you cannot shuffle only the Inn into your draw pile, and thus the Inn would have to stay in the discard. (The instruction is not "put Inn on top of your draw pile. Shuffle your draw pile.")
Yes, it must be. "Shuffle the cards into your deck" must be shorthand for "put the cards into your deck, and shuffle it." Anything else is madness. "Shuffling cards into a deck" is not defined as an action you can do in Dominion, and also doesn't exist in real life, except maybe by accomplished close-up magicians.