Florist struggling with shipping settings

We are a small florist who typically uses a flat shipping rate for in the city area and a higher rate for outside of our city from mon - sat. Our usual deliveries are taken by courier or walked if the delivery is close by. For Mother's Day being that it is a Sunday we are looking to have a different shipping cost as we have to have another staff member on with the additional cost of the fuel etc.

Has anyone found any way to add a variable price for different dates through the shipping at all? 

We have assessed adding product variants for the shipping but do not believe this to be possible for what we are trying to achieve.