This is a telling of a Yamanba story in Hakata dialect (Kyushu) I think. But that’s only from an internet search of なさい→んしゃい and を→ば, so feel free to correct me if you recognize the dialect.
The radio show is called Toshio Ozawa’s invitation to folk tales (小澤俊夫 昔話へのご招待 Toshi Ozawa -invition to the folk tale-) and the teller is Itsuko Matsuzaki. Most of the episodes are downloadable through the linked web site or a podcast on iTunes (including this story). I did the subtitles, and I’m not an expert on dialects, so be forewarned there may be some minor errors. If you speak much Japanese and enjoy folk tales, please check out the show! It’s usually in Tokyo dialect. Mr. Ozawa is a folklore scholar and has studied European folklore in Germany as well as traditional Japanese folk tales. He’s a groovy guy!