If your son ran a business, he need to report that business on his own tax return. It does not matter if he receives a 1099 or not.
If you want to avoid a notice from the IRS asking about why you did not report the income from the 1099-K on your tax return, you might consider filing to show you had a business that had that amount of income, then enter an equal amount as a "other deduction" (so the net amount is $0), and call that deduction "Nominee income to [your son's name]".
