No, you definitely should not have used "have" instead of "has" in your sentence. However, you could have used "would have" or "will have".
I might suggest a bit of rewording at the beginning of the first sentence:
"Unfortunately, I have neither the data nor the expertise to address your question. Perhaps John will have a more useful answer. "
If you are confident that John will be able to help the person, you could use something like this as your second sentence:
"However, John should be able to help you."
Student or Learner