Only a few titles at the moment, since this list only has movies I’ve watched.
Needs more than one or two songs woven throughout and sung by nightclub singers (such as in Tokyo Drifter), although I’m bending the rules a little for Karaoke Terror.
Includes the 1962 version of Black Lizard (Kurotokage) directed by Umetsugu Inoue and starring Machiko Kyō:
Feel free to suggest more movies for the list!
ETA on 2/26/2018: Not yet on MUBI: Tokyo Mighty Guy (1960,Tokyo no abarenbô)