The first and second generation iPod shuffles are only designed to be used with one iTunes library/computer (they don't have the full manual setting that allows them to be used with multiple computers that other iPods have). The only way to link your iPod to the new library is to sync the two and reload the iPod from your new iTunes. If you don't have the songs that on the shuffle in your new iTunes you can however if you are careful copy the songs from it and once the original songs are in your new library it will be safe to sync.
Retrieving songs from a shuffle is a bit different from retrieving songs from a regular iPod. When you connect to your computer you get the message that it is linked to a different library and asking if you want to link to this one and replace all your songs etc, your reaction of course is to press
"Cancel". As soon as you connect a shuffle and choose "Cancel" when you get the "linked to different library" message the iPod will disconnect. For a shuffle follow this process:
1). On your Windows desktop go to Edit>New folder and add a folder to receive the songs from your shuffle.
2). Download SharePod from this link:
SharePod
3). Connect your shuffle to your computer. While connecting the iPod to the computer on Windows with iTunes installed hold down the Shift + Ctrl keys together. Your iPod will connect but iTunes won't open, the hardware icon should appear in your Windows system tray.
4). Open Sharepod, it should have picked up the presence of your iPod and show all the songs on it.
5). Highlight all your songs in the program window (click on the first song in the list and hold down the shift key, click on the last song and all the songs in between will be selected).
6). Click Copy to PC (the icon is in the top left corner) and choose the folder you created on the desktop or simply drag the songs from SharePod to the folder:
SharePod - Copying tracks to your PC
7). When all the songs have transferred close SharePod
8). Disconnect your iPod by right clicking on the hardware icon in your system tray:
Safely Disconnect IPod
9). Check the desktop folder and make sure all your songs are there.
10) Open iTunes and go to File>Add Folder to Library, navigate to the folder on your desktop and add the songs.
11). Connect your iPod. When you get the message that it is linked to a different library and asking if you want to link to this one and replace all your songs etc. Choose "Erase and Sync", iTunes will reload your shuffle with the songs you recovered and link the iPod to this new library