I was tired of not being able to skip with a keyboard shortcut if Spotify wasn't focused, so I created an Alfred workflow to let you do exactly that.
I recommend using the keyboard shortcut ^ + ⌘ + →/← for skipping forward and backward as it is already set in Spotify and is most likely not a shortcut used by other apps.
If you enjoy this workflow or rely on it to enhance your Spotify experience, please consider donating. I'm a college student creating and working on open source projects such as this one for free to enhance your experience on your Mac, and I hope you enjoy it.
If you have any questions, open an issue on GitHub. I hope this workflow treats you well!