shai-ga,
I would not leave the fretboard overhanging on the edges, you'll be unhappy with it in the end.
Mikey R and martinedwards have given you a really good suggestion.
Basically, you are going to glue two thin strips of wood down either side of the neck (contrasting woods will make it look really cool). You will probably want to cut off the sides of the headstock (making your cuts following the taper of the neck) so that you can plane/joint all the may down the neck without the heastock getting in the way of the tools.
Once you have made the sides of the neck appropriate gluing surfaces, glue on the side pieces of wood. Make sure to use lots of clamps and many smaller cauls or one realy long caul. You may also need to put stopper blocks at either end just in case the side pieces want to slide along the taper of the neck when clamping. You can always make the side pieces thicker than you need and then plane them down to the neck thickness you want as well. You may also want to make them wide enough so that they cover the sides of the heastock.
Once you've glued on the side pieces, you can re-glue the "ears" back onto the headstock and viola, you have a neck that is the right thickness with some added accent.
If you have any questions, just let us know!