MarkB
Legend
In your situation I'd try the simplest and least intrusive approach first. If no one else wants to initiate an exchange, then go ahead and speak first, but hand off the conversation as soon as possible: "Your majesty needs us to recover a magical artifact? Bob here is our mage, I'm sure he has some questions for you." IME once the conversation is started things usually go pretty smoothly.
That's the only way to go, really. Whether you're playing your character and speaking up, and getting the party in trouble, or playing the fool to guide the other characters by asking the leading questions, it's still you doing the talking, and that's never going to change the table dynamic.
If you keep dropping the ball back in the hands of the players whose characters are built for these situations, then eventually they may pick it up on their own initiative.
If you're playing the low-Int barbarian, it's pretty easy most of the time. Anytime someone talks to the party, just push the designated spokesman to the front (or have everyone else step back) and say "He talky guy. Talk to him!"