Early Startup Employee Dispute

In March, John starts thinking of starting a new company. Shortly after, Mike, who is potentially interested to join John’s company as one of the first employees, starts helping out casually, and as an IT guy, takes on the setup of the hardware. In June, the company is incorporated; but soon after, Mike, considering the situation too risky, decides not to join John’s company and takes another full-time job. He then sends an invoice to John for his work, with a clearly inflated number of hours. Having at heart to be fair, John reviews the hours, and even though the work is subpar, he writes a contract for about two thirds of the hours originally claimed by Mike (John is in a position to prove that the hours were inflated thanks for computer logs and emails), and agrees to the rate of $75/hour that Mike asked (above market rate for the tasks at hand); he sends the contract to Mike. Mike refuses to sign claiming that he never agreed to a consultancy agreement, and demands to be paid under the table, claiming that this was the original agreement (there was, of course, no such agreement in place). He threatens to sue the company if he doesn’t receive payment for the invoice he originally issued (at the rate he determined himself).
What is the best path forward for John? What should John do knowing that paying a large lump sum “under the table” is likely to negatively impact his ability to take on investors?

If Mike does sue, then there is no way that his work effort and any payment for it could any longer be considered "under the table."

I don't think John necessarily needs a signed contract in order to pay Mike (verbal agreements are still "contracts"), but he does need Mike to supply the information on a form W-9 (mainly Mike's taxpayer id number) so that John can properly report the payment to the IRS and on his corporation's books. By sending an invoice, Mike is implicitly (well, even explicitly) indicating that he is indeed a contractor and not an employee. The disagreement then seems to be over the number of hours. John could ask Mike for documentary proof of the number of hours that Mike has claimed, and/or explain to Mike (and provide the evidence) of how John determined the number of hours. In the meantime, John should hold fast on his offer of payment based on the evidenced number of hours, subject only to getting the w9, not necessarily needing a signed consultancy agreement...