I would either say Hatate doesn't have a theme, or have Youkai Mountain be both Tengus' theme. Plus, Aya already has Wind God Girl from PoFV/StB.
Speaking about characters without themes, quite a few characters from the PC98 times, Daiyousei, Koakuma (although those two have their stage themes to work off of), Lily (Same thing), and other midbosses with no stage to themselves don't seem to have "themes" other than their stage theme.