I used to work for a consulting firm and one of my fellow consultants, a guy who went on to some measure of nerd fame as a DevOps evangelist, used to set up his consultations by saying "I don't know everything but I work for a company that does. If won't have an answer for every question, but I'll get an answer for you if you give me time."

That doesn't match your context perfectly, but I think it does communicate the importance of managing expectations.

I'm pretty good at thinking on my feet, but I'm also not above changing my thoughts once I've examined a situation in detail. So when asked a question on the fly, I'll respond "my gut tells me X, Y, and Z but I'd like to think about it a bit and get back to you". If you do that, it's important that you follow up with some real thought and structure that provide real value. The confidence comes not in how you ask for time to think, but in your audience knowing your followup will be worth their while.