In order to change the default navigation buttons you should redefine the style of our CarouselItemsControl. Although it sounds scary it is actually pretty easy since the style of the CarouselItemsControl is very simple.
I have attached a sample project that demonstrates how the navigation buttons can be restyled.
The carousel navigations buttons are actually buttons of a scrollbar and in order to customize them you should create a custom ScrollBar style.
the Telerik team