If it is a static recurve you don't need the sinew on the non-working portions of the tips and it only adds unnecessary physical weight. Also, the sinew can pull off the inside curves as it dries. I leave the last 6" of the tips free of sinew and skins because it isn't needed there and to prevent excess wear on the string. A simple wrap at the end should hold it fine. I usually do a sinew wrap over the end of the sinew and a silk thread wrap over the skin.
You do, however want sinew through the handle area. I neglected to do this on the last two sinew backed bows I build and lost some of the zip I should have gotten plus both bows began to take set in the unsinewed handle area or at the fades.