I am thinking more along the lines of a scroll bar to the right of the component bar and/or automatic scroll on parts selection, but a button to expand the area should work too. It might even be better, since it gives the player a better overview of all the parts.
The scrolling with the mouse wheel suffers from the same problem as the mouse wheel has in all the list: responsiveness. But SD is aware off that, so a fix may be coming (soon pretty please).