A forked whitetail antler is the right size for small hands. Size up to a muley shed for larger hands. Cut off the tine tips and file grooves near the ends.
For the bands, I like TheraBand Gold. Double them to increase the poundage for squirrel-thumping velocity. Attach them with smaller strips of the TheraBand. Wrap a strip six times around the slingshot band where you made each groove. Place a doubled-over piece of thin string vertically (up the tine) over the wrappings and make two more wraps. Push the end of the TheraBand strip through the string loop and use the string to pull the end under the last two wrappings (making a nail knot). Trim the ends.
Use the same method to attach the band ends to the pouch, which you can cut out of leather or canvas. Be sure to make the bands the same length.
Use 150-grit sandpaper to remove burrs. File finger grooves into the handle. Apply a tung oil finish.