The Zip does not have a wheel just a 4 corner square that you push one of 4 ways to control. Quick audio is not good but the patience to finish things is needed a lot less and that makes it worth it for me.
I think maybe I had the same problem originally. After you click Yes, DELETE (middle, silver button) you will come to a second screen where the default response is "No." If you are like me, you have immediately simply pushed the middle, silver button again, thinking, Yes, I want to delete this. But instead you need to take an additional step. After you click on Delete Song, you come to that second screen, and there you need to click on the upper button (the symbol is >||), which moves the cursor up to "YES." Then you hit the middle, silver button and the song is deleted!