You're "fighting the system" unnecessarily. Let TurboTax (CC) do it's job. There's no advantage for using Schedule C-EZ over Schedule C. The TT fee is the same. The risk (or non risk) of an IRS audit is the same.
Although it may be news to you that you “have a business” (and most of the other people who get their first 1099-MISC); The IRS considers anything in box 7 of 1099-MISC to be self employment income. Enter the 1099-Misc income, at Other Common income / income from a 1099-MISC . TurboTax (TT) will complete Schedule C or C-EZ (if appropriate) for you and allow you to deduct any expenses associated with this income. You'll also have to pay self employment tax (social security & Medicare) on any profits greater than $400. These types of payments are frequently done this way. Your "employer" is not the only one.
The IRS also considers undocumented cash income (no W-2 or 1099-MISC), for work performed, to be self employment income.
You cannot make manual entries on the forms with on-line TT. But, it appears that you are using desk top/download software. To make manual entries, you right click on each box/line and use the override feature.
