I don't know if a Ladies Pro Wrestling promotion counts as a band, but at the 7:25 point of the video the fighters "make up" after fighting and idol sing a song along with Hello Kitty.
Notes:
When Ice Ribbon first started (around 2006) the Dojo didn't even have a ring so dojo shows were on a mat with other girls surrounding the ring acting as ropes.
Matsumoto Miyaka introduces herself as "ichiban kawaii" and pulls out one of her moronic (for a wrestling match) dance poses in the middle of the fight.