Excluding skins without a music obviously, there are some skins with a dance music, but the volume is too low to be heard, and it feels akward.
Here's a list of skin who could have a dance music volume tuned up.
+++ (Toned up, the sound is very low)
++ (Toned up a bit, you can hear the music but it could be a little louder to match the others)
+ (Toned up a very little)
Odyssey Kayn: ++ (expecially the initial part)
PROJECT Vayne: +
Pulsefire Caitlyn: +
High Noon Lucian: +++ (a friend that plays this skin a lot never heard the dance music)
Infernal Nasus: ++ (Expecially during R)
Battlecast Cho'Gath: +