I have repaired some wallboard joints and paint peeled areas with wallboard compound and now want to sand these areas smooth. I would like to know if it is possible to do this dust free after the wallboard compound has dried?

If you have used a good sized knife to lay down your joint compound you should be able to do a small scraping action to remove the bumps and then wipe several times with a well dampened sponge. I almost never sand joint compound. Wipe back and forth with the sponge and only slight pressure. This kind of melts the surface of the compound and lets you redistribute some compoind to make a great blending of the surfaces.