IRS Form W-9 has nothing to do with taxes or exemption codes for anything, from anything. It's a "request for taxpayer identification and certification" and that's all. https://www.irs.gov/pub/irs-pdf/fw9.pdf
That particular form is used primarily to get taxpayer identification information required by law, by the person or entity paying them.
As for exempt entities (not individuals) you'll need to read page 3 of the instructions for guidance on that.