It is quite possible to replace the tube without sewing the whole tire back up.

Open a spot about two inches long, cut the old tube and pull it out. get your new tube, cut it and feed it through the tire, glue the end back together. A good latex tube will not be difficlut to do and there will be noticeable lump where you glued the tube back together.

A product such as goop will work well for gluing the tube.