Hi Nathan J Pledger,
This is possible, you can create new button that replicates the default ones, and insert it in the table that holds the buttons of the RadListBox.
I have prepared a demo for you, where the approach is demonstrated. As you will see, there are 3 buttons in the demo, the first 2 are default buttons - the reorder ones. The third is a custom button with very much the same look, the only difference is that he don't have the background arrow image. When you click on the custom button an alert pops up (you can implement your logic instead). Is this what you are targeting?
the Telerik team