If you are able to connect the shuffle to iTunes and show its list of songs, it may be best to take a screen shot of iTunes window at max size. Scroll the list and take additional screen shots as needed.
NOTE: There is a command in the menu bar to
File -> Library -> Export Playlist...
Give this command with the shuffle's Music list selected in the sidebar. However, this command is meant to create a text file that is later imported into iTunes, so it is not formatted to be nicely readable to human eyes.
iTunes 11.x may hide the sidebar (along left side of window). To show the sidebar, from the menu bar, under View, select Show Sidebar. To show the list of songs on the shuffle...
• If the shuffle is 3rd or 4th gen, find the shuffle in the sidebar, under DEVICES. Click the small triangle to the left of the shuffle's name, to drop down its content list (indented below the shuffle). Click on Music there.
• If the shuffle is 1st or 2nd gen, the shuffle itself is one playlist. Select it in the sidebar, under DEVICES, so that its Settings screen is shown to the right. Toward the top, where is says "Settings," click on On This iPod (to the right).
You can actually off-load the song files from the shuffle. You cannot use iTunes to do this (except for songs purchased from the iTunes Store), but there are third-party methods and utilities that can transfer song files from iPod to computer. If you do an Internet search on something like "ipod transfer," you should get some links. (The CNET article seems to be popular.)
Once the song files are on the computer's drive, I suggest you create a new playlist in iTunes, and name it appropriately (like "Old iPod Songs"). Show the song files in an Windows Explorer window, and drag them to that playlist in the iTunes window. iTunes will add the songs to the (general) iTunes library, but that playlist will only show the songs that were on the shuffle. And you can actually play the songs for a shot of "nostalgia" (not just look at their names).