I normally use wooden trim to hold glass in however if you have only 1/4" by the time you put glass in there wouldn't be room to nail it. You might fashion some screen molding with a lip to extend over the glass and mount it to the back of the door if trim on the back wouldn't hit anything. You might use glazing points to hold the glass in and then use color caulk to cover the edges. Another option would but to use the points and put a piece of wooden glass stop over them with hot melt glue. You could also use the old fashion method of glazing points and glazing compound. The compound can be colored to be wood color with a universal tinting color.