It appears that this is specified as part of the DefaultCalendarView type, in the nested DateCell class's update(Date) method. I don't see an obvious way to override that, nor to replace the DatePicker.StandardCss type (package protected). Instead, you might implement CalendarView in your own way (perhaps copying some of or all of the existing content in DefaultCalendarView), then subclass DatePicker to pass your own instance to the protected constructor that takes a CalendarView instead?
As another option, can you clarify what additional styling you are trying to add? It might be possible to use the existing CSS styles to do this, or find another way to produce the same effect you're after?