Wow, the art style is amazing! And the music fits so well with the artistic style. I love how you incorporated more than one background track to make the run feel new in a way.
I think for a game with simple mechanics like this, it could be satisfying to see some visual impact on the hits such as impact frames or freeze frames when hitting the rats or bats or cheese balls. I also noticed that the animation of the swing doesn't quite match with the mouse click input. Slow animations frames like this can make player inputs feel delayed and laggy. I think simply removing initial anticipation frame would fix this.
For combat, it would be great if there were a downward attack. I find myself landing on rats more often than I'd like too. Darn rats! Simply being in the air seems to punish the player.
Nevertheless, keep up the great work and love the art!