My opinion, take it for what you will:
I think as long as the character is conscious/alive, the player should be given a choice as to whether they want to speak up.
When they speak, have the guard strike them, then roll damage (probably a d4, but could be a d3). Tell them to mark off that amount of damage on their sheet. When they reach 0, they go unconscious. (You know that this is just "temporary" damage that causes them to go unconscious, but they don't need to know that right now...and bonus: you don't even have to say they're passed out..."You see Archie slump in his stocks, a gash on his forehead trickles blood.")
Consider having the guard say, "Quiet your filthy mouth before the queen!" or some such thing so the players have some idea why they're being struck.
Consequences:
This will allow a stubborn player to keep talking if they'd like, and eventually they'll get knocked out and shut up.
Players will know (or at least think) you mean business and that you might be willing to kill them right now in the opening scene.
Players have more choice and control.
A knocked out player can later be doused with water. You tell them that their hit points are back, but they have a penalty to their Wis/Int for a while due to a pounding headache.
Consequences of the saving throw route:
A player fails their saving throw and you tell them they've been hit on the head and can't talk. Player says, "What? Why can't I talk? Did they damage my throat or mouth? When can I talk again? Can I spit? Can I make growling noises? Can I scream nonsense?"
All the players pass their saving throws and just keep talking to the queen as much as they want.
