Stop in for a cup of coffee

Cool

I'd lean toward a shelf across to support. You'll have the raw edge to deal with, which you could stain if it's solid wood, or put a piece of trim off it's press board, just to seal it up.

Other option would to be remove it all, then, if the wallpaper is just that strip, remove that bit of paper and the top board to go with a skim coat and and ceiling paint