Certain things that feel wrong are the right thing to do. I do not know is almost always the right thing to say if you genuinely do not know the answer to a question. It wasted very little time and gives them the option to give you advise or order you. Then you choose to act on what they say or not.

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You don't need to feel stupid. You don't need to feel compelled say something unrelated or actually wrong. If you have relevant information you can say "All I know is..." followed by the briefest possible summary of what you for certain know. If you are not 100% certain tell them roughly how certain you are. They will most likely ask questions if they think they need more details. Further, if you think of something else that is relevant offer it at the earliest convenient or appropriate time.

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Don't overthink it just be honest and clear.