All I can suggest is using the tiniest needle your thread will allow - like a size 10 or 12. I'd stick with sharp needles because ball point is usually for stretch fabrics like knit. If you have a problem with fraying - FrayCheck is marvelous. It works like clear glue and stops the threads from fraying.
Also, since it's "only" a costume, you could try using a longer stitch so you don't have as many needle holes.
Sometimes just ironing it afterwards helps a lot too.