This is actually already possible if you don't mind editing the config file yourself, I just haven't had time to expose the functionality in the UI (plus it's not had much testing, due to me not having a spare microSD card).

Just edit .local/share/harbour-cutespotify/CuteSpotify/CuteSpotify.conf and change the dataPath value to the location you'd like it to store files.

It won't clear out the old files, so you'll need to do that manually.