I did something similar to Umi on one of my boats, for the cap rail. One strip the width of the rail and two smaller strips that fitted under the sides, this then hides the join on the side edge which is less visible than it they were on the top.
The advantage of either method is that you can go around bends in the railing. Do the straight part of the run first, and let the glue dry. Then do a few inches of the bend, glue up and let it dry, then do the next few inches etc. This way the cap rail can easily follow the curves of the deck/hull/bulwarks, without twist and distortion. It really was much easier than I thought it would be.