Yes, you can drill a hole in the pick and string yarn or a thin piece of leather through the hole. If you don't have a drill you might want to try just gluing a piece of necklace cord to it with a dab of super glue.
Just make a tail that's about 1 inch for every 2 stitches. Any craft store that sells knitting needles should have circular needles that are just the same size as...