That is the magic word, to me. If the entity being paid could not have others work, (and also whenever they elected, not for a specific amount of time within a window, and did not have other clients, business license, business insurance, etc.) then employee is proper.
In the OP, the deduction for a day off is employee all the way.
Probably not a huge chance of getting caught, but I personally would not be comfortable with a 1099 in the OP.