Need help with preserving attached hidden information despite shuffling

The problem is that you want the players who choose such actions to be hidden in the mass of players who chose "normal" and general actions.
If a player has to do anything the others don't do while choosing their actions, it will be easier to guess he did it.
You could force everyone to do "as if" they had to choose a target, but it will take time when none of the players has to choose any target.

Coming back to your problem, I can imagine two ways of doing it.
-The cards could have a designed target on them already, such as "the player with the highest score", "The player with the most cards in hand", their variations ("The third player with...") and others. The problem is that this doesn't allow for the players to choose their targets anymore, but on another hand, they can go back to other action cards if they are not happy with it.
-The players can write on the cards which player the target is. For example, if each player is designed by a colour, you could have squares of each colours, and the player would just put a cross next to the one he wants. Of course, the cards should be in a plastic that allows to erase easily the markers and if a player writes on a card while none of the others do, everyone sees him (like i said).

I think that my first idea is better, but I'm sure someone will come with an even better one.

I can't think of any game that has used them, but there are inks that react to the heat of your body-- you press the card between your fingers and the temperature rise causes the ink to change color. Eventually, when the card cools, the ink returns to the original color. I don't know how long you need the decisions to stay visible for; if it's for a long time, this might not be a viable option, but it's worth looking in to.

I'm fairly certain you've overspecified the problem, and as such, even if you can find a physical solution, chances are it will be a pain for the players, or easy to cheat (intentionally or accidentally), or some other thing.

What if instead you played action cards directly onto a target, face down into a pile? Then, when a player has accumulated 5 (?) cards, shuffle, reveal, and resolve. In this way, players maybe get some inkling of who the traitor might be, depending on who played a card in your direction -- and the traitor will have to be careful not to pile on a single player (whereas the other players may want to encourage this to make it easier to ID the traitor, although it also means one of them will suffer more, etc)

Similar to the previous idea above this.

You can give each player identical envelopes.

Each round players will pick an action that can be numbered and then players will have extra cards that specify which action is being chosen and another card that specifies a target.

So for example say you have a card that has 3 actions or something, they player choosing this card would also play a card that has the number 2 to imply option 2 is being picked, lastly if a target is necessary, the player also slips in a card signifying a player (color, "character" name, etc.)

Then these envelopes are shuffled together then each are opened one at a time and resolved.

As a result of this system, you can have it so that the cards are returned to their envelopes, shuffled, then redistributed to each player randomly, giving players new cards and limiting their options.

Other options for cards can be things like group choice or random choice.

I do not know if this may impede your design in any way but those are my 2 cents. Hope it helps!

Inspired by Sheriff of Nottingham deception card game.

Instead of making every player a target on every action card, you could specify 4 targets on each card, one option on each corner. For now lets just number the players 1-7, so some cards have 1,2,3,4 on the corners; and some have 2,4,6,7; and so on; with an even distribution of targets. Numbers might be green if they are to be resolved openly, or red if they are to be resolved after secret selection.

Each player has a a single card that has a giant arrow pointing to one corner. Players simply select the action and then orient their option card to point to the corner showing their intended target. They shove these two cards into a shuffle-able sleeve and submit.

The pile in the center was assembled in a similar way, action cards drawn randomly face down; option cards drawn and randomly rotated (spin) and sleeved together.

The sleeves are shuffled ad then as actions are resolved, the option cards are discarded and whoever needs one simply takes one as they are all the same.

The biggest problem here is having sets of cards that play with 4+, 5+, 6+ players and so on that have an even distribution of targets. Oh, and square cards!

I like @Jwarrend's solution.

Sleeves! I never thought of using sleeves as part of the game mechanic, but it seems so obvious now. Transparent cards are cool, but you wouldn't need all that. If the question just comes down to attaching a choice to a card, sleeves are a pretty simple way to do it.

This is how you do this:

Option 1:
Give each player a set of cards, with a card for every action, and a card for every viable target of that action.
Action cards have a black back.
Target cards have a white back.

Procedure goes like this:
1) Players select the (black-backed) Action card they want to use.

2) Players then choose the white-backed Target cards and place them under their respective Action cards, forming a 2-card stack.

3) Collect these stacks into a single pile to make a small deck. (In a 4-player game, for example, this will be a stack of 8 cards, with alternating black/white backs, and a black card on top.)

4) Then, one or more players will cut the deck as many times as they choose, but always so that a black-backed action card is on top. This will keep Action cards always directly above their selected Target.

5) Reveal pairs of cards from the top of the stack, resolving each Action sequentially.

6) Reseting the system depends on the type of game. You could immediately shuffle together the used and unused Action and Target cards, and deal out another set to each player. Another option is to play another few rounds with the remaining cards, which could have its own interesting gameplay dynamics depending on how the rest of the game works.

Option 2: (more expensive)
High-tech production way with punchboard––
Same basic idea, as option 1, but with punchboard tiles for Actions and numbered chits for Targets.

Give players a set of a punchboard tiles for each Action, with a hole in the tile for a chit. When selecting Actions, players choose the desired Action tile, and place a Target chit in the hole. (Friction should hold the chit in place.) Then, shuffle the tiles together and reveal them one-by-one, with each Action being resolved based on which Target chit is in the hole.

This functionality is something that we did in I, Spy.

How about this use of sleeves: Everyone has a full set of target cards -- one for each player. Every turn they put ALL their target cards in the sleeve, such that they player they are targeting is in front and displayed through a small window in the sleeve. The sleeves are turned in and shuffled with the window side down, and just need to be turned over to reveal the targets.

After that round is resolved, everyone gets a sleeve back, which, of course, has target cards for all the players.

You could even have selected cards of two different types, for example an attack type and a target. All the target cards have a hole in them in the same spot, where the attack type icons are. All the attack type cards similarly have a hole in a different spot, where the target icons are. The sleeve has holes in both spots. When choosing the attack, a player chooses an attack type and a target, puts those in either order in front and all his unused cards behind them. Both attack type and target will show through the holes in the sleeve.