This is fun, and an utterly fascinating challenge of just the kind Thor likes best, and the storm still patiently gathers above their heads, and soon she will have lightning to play with.
They've accumulated a bit of an audience by now, and spectating Asgardians are somewhat confused about why Thor is fighting a magic dog, but she's definitely having fun, so no one's about to complain.
Lightning! Hammer! Dramatic swirling clouds!
And if she can get Huan between the hammer and the ground, perhaps she can do more than fling him a ways—?
Dog and face probably aren't a good combination. Thor dodges, and swings the hammer, and summons more lightning from the sky.
She's flung a considerable distance, lands awkwardly, recovers in the next moment, and takes to the sky. Lightning? Lightning.
She soars up and up and then comes back down again, like she did at the beginning of the fight, but much faster and wreathed in crackling lightning.
Hammer! Lightning! Gleeful laughter! (The gleeful laughter is not combat-effective but it is still very important.)
The force of impact is immense. Both combatants are thrown away from it, Huan back down to the ground, Thor back up to the sky. She turns around and comes down again immediately, sending lightning chasing after Huan since lightning, unlike Thor, is still faster than a blurred dog.
And another impact and she circles back again. They could keep going like this for a while, Thor trying to maneuver to smash Huan against the ground again, Huan shrugging off lightning strikes in the meantime, extensive damage being done to the surrounding landscape but nothing reaching as far as the spectators.
Thor has picked up on enough about magic music to be wary of this development but she doesn't have a good way to reliably interrupt him, at least not if lightning alone won't do it.