Is there a way to "turn off" the visibility of the Turn Order for players?

I am looking for a way to either temporarily turn off my players' ability to see the Turn Order, or at least render them unable to mouse over it and see which token's turn it is on the map from the outline. I have a large Doppelganger encounter in mind, with the doppelgangers using multi-sided tokens that have all of the player-characters' faces available, with the idea being that once the battle starts, they will all begin changing their faces to that of various characters to sow confusion. Of course that's rather hard to do when all the players need to do is mouse over their names in the Turn Order and clearly see which is the "real one". So is there a way to temporarily disable their ability to see the turn order, or make it so they can't easily figure out which token's turn it is?

Nothing straight-forward, there are workaround methods of varying complexity. Easiest way to me is, use Custom initiative item for every line instead of the tokens. If you need them to roll init from their token, next step would be (as GM) make a Custom initiative line and copy-over the init number that they rolled, then remove the PC from the init order.  Example: Bob rolls init 6 Jenny rolls init 5 GM adds "Bob (The Real Bob???) 6" as a custom item and delete PC bob from the Turn Tracker.  GM adds "Jenny (is it the real Jenny tho?)" 5" as a custom item and remove PC Jenny.  Go on adding additional custom lines for the dopplegangers and name them similar or same. 

Hi Shard! You could accomplish this by having them all roll initiative, and then duplicate the page, moving the flag to the duplicate. Y ou will still see the turn order, but it will be hidden from them, since players cannot see tokens that are not on their flag page, or on the GM layer. You should have a turn order that is visible only to the GM.

When I don't want the PCs to know the order of attacks but still have their opponents visible on the map, I'll place duplicates of the NPCs tokens on the GM layer and use those hidden tokens to roll the NPC's initiative.