In this particular scenario, do you believe that a person chooses between cleaning (an unskilled job) to cooking (a skilled job) based on the wage that is paid?
Either the person is unskilled; then they have no choice. Or they have the skill to be a cook; then they presumably have the skill because they like being a cook, and will certainly prefer to do that over cleaning even if both are paid the same (in fact, they will probably prefer cooking even if it were slightly higher paid; wages only start coming into consideration when the difference is larger).
Now you might argue that people will be deterred from even learning to become a cook in the situation you have outlined. That is doubtful, because again, price plays a much smaller role than you might think. But even if it were the case, the wages of cooks would eventually rise above the minimum wage if demand for cooks is high enough.
It is a mistake to assume that there is always a God-given market price that is the "right" price for goods to have. The development of prices is always a negotiation within society. In the case of the minimum wage, society says that labour should have at least a certain price, because that is the morally right thing (and also avoids certain externalities that opponents of the minimum wage like to ignore). If society agrees on that, then minimum wage is efficient by definition.