I always smoke the trimmings. Since they're smaller and will generally be finished first, they make a great snack for the cook to munch on. After the meat's pulled from the cartilage, they're also great for throwing into a pot of beans or putting on a bun.
As for your second question about what to do with the skirt, it's just like on prom night. The skirt comes off.
Hope this helps.
Ken