Doing a Restore deletes everything, but that's not the best way to manage songs on your iPod. 🙂
In iTunes, select your shuffle so that you see its settings screen. I'm assuming you have the current 4th gen shuffle (or 3rd gen). If you have an earlier model, post back with the type. Procedure for 1st and 2nd gen shuffle is a bit different. And this is for the latest version of iTunes.
On the shuffle's settings screen in iTunes, along the left side of window (in the sidebar), under On My Device, click Music. To the right, you see a list of songs currently on your shuffle. To delete a particular song, select it on the list and press Delete on keyboard. You can do this with more than one song selected. If you want to delete all the songs, you can do a Select All (from menu bar under Edit or Cmd-A on keyboard).
NOTE: If the song list is "greyed out" so that you cannot select anything, please post back. That means your shuffle is set up for automatic syncing, and there are a few other steps.