How do I delete songs hidden in the icloud without enabling itunes match.

I have two laptops that are exactly the same. On one I was able to send all the music I didn't want anymore to the recycle bin and then empty the recycle bin. On the other computer I was only able to "hide" the songs on the cloud. I don't see an option to delete and I only see discussions about how to delete from the icloud when itunes match is enabled. I do not subscribe to iTunes Match. Please tell me there is a way to delete these songs because by just hidding them they are still accessable to be redownloaded, which defeats the purpose.