you can burn the songs you want to sync onto a CD and then download them to your iPod from the harddrive
Plug in your iPod and don't press "Sync".
first thing is when you connect your ipod highlight your ipod and select music and check manually manage songs and there you go you can sync songs without syncing to that itunes library.
See links to Apple.com
You have to sync it because when you sync it go from your computer to your iPod but if you have an iPod touch you can download songs from your iPod's iTunes store.
get iexplorer
go on extras on your ipod nano, go under voice memos, record your songs on voice memos
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Before connecting the iPhone to the different computer, in iTunes go to Edit>Preferences>Device>select Don't Sync Automatically. When you connect the iPhone go to Pictures tab and Other tab (on top of the sync screen) and disselect Sync Pictures and Sync Contacts. Then press apply (bottom right corner).
Try unticking all the songs on Itunes. And add tick ONLY the songs you want to sync into your ipod. Itunes will only Sync the ticked songs. The rest of the songs on your ipod wont be erased.
You can download the free trial of a program called Music Rescue, I think it's on download.com. The free trial will tell you to buy the program after it loads up 100 songs, but when that pops up just click cancel or X out of the message.
If your songs are already in the new library, you will not loose any of your songs.
oxymoron, formatting a drive is erasing the data.