When you believe that spanking (or, more broadly, unrelated punishment) is not appropriate parenting, punishment is not part of the toolbox. If you believe that you shouldn't spank, it doesn't matter what personality children in your care have.
I managed 2 daycares and 3 of my own children without spanking as a discipline option. I didn't have to revisit my decision because 1 of my 3 kids was "strong willed" or any of my daycare population was "strong willed".
I run a tight ship, with high expectations. Indeed, some posters here would find my rules and expectations to be too much. And I did/do it without spanking or arbitrary, unrelated punishment.