"Would you attach the 1099 with the hand-masked out partial SS to the return?"

No. The IRS already has a copy. It isn't meaningful to the Sched C.

If your client's client had issued this 1099 and your taxpayer's tax filing never included any business income, then the IRS would have something to pay attention to.

If your taxpayer was their employee, the "employer" cannot have payroll and employee reporting using only their SSN. That changed years ago.

You are worrying needlessly, because the issuer is not your client. Give your clients better guidance, and you have nothing to worry about.