You can use the RadRadioButton.IsBackgroundVisible property and set it to False to make the button transparent. You can also define an Image object as the Content of the button. I attached a sample solution demonstrating this approach.
If you still need to edit the default style or ControlTemplate of the RadRadioButton you can take a look at our documentation describing how to customize the control.
Let me know if that helps or if you need more info.
the Telerik team