The first gen shuffle holds just one set of songs, so it does not load "playlists" like the current shuffle.
Here is how you change what is loaded on the 1st (and 2nd) gen shuffle. If you are using the latest version if iTunes, you should show the sidebar, if it is hidden. From the menu bar, under View, select Show Sidebar.
Connect the shuffle and select the shuffle in the sidebar under DEVICES. Over to the right, click on On This iPod next to Settings. This shows a list of songs currently on the iPod. Select the song you want remove and hit the Delete key on keyboard. Confirm you want to Remove. You can do this to one song, or a selection of songs, or the entire list by selecting Select All from the File menu.
NOTE: You can use the Autofill feature at the bottom of this list to quickly load the shuffle.
To load new songs manually, drag them from your iTunes Music library to the shuffle in the sidebar.