Hi,
if you sync you iPod with iTunes, all the music in the iPod will be deleted.
what you need to do is to click on your iPod icon when you connect it to the computer and then check "Manually manage music".
then you need to create a playlist, put all the songs you want to add in your iPod, then under the iPod click on Music, and you will see "Autofill from:" below the window.
select the playlist yu created and click on autofill.
thus the songs will be added without deleting the ones which were already on the iPod.
it is recomonded that you update the iTunes when you are prompted to do so.
thus you can get more features.

It is safe for your iPod as long as turning off iTunes or its auto sync. if you are using the iPod on more than one computer,then set the iPod to "manually manage songs and playlists"(edit->preference->device->disable the auto sync for all iPod and iPhone)and this will keep it from automatically synchronzing with iTunes and erasing all of the songs on the iPod.
In your case you can sync your iPod to your existing iTunes in your old computer and then plug it to your new computer. At this moment you need a third patry program to transfer your iPod's songs out to the newly iTunes on the new computer and then sync your iPod to the new iTunes. For the transferring tool i recommend Aniosoft ibackup. It enables you to transfer iPod's music and other content to any storage device and iTunes as well. And both the backup in the storage device can be recovered and restored with no any change and no any risk.And the data in the iTunes is quite in accord with the iPod's data including its playlists,rating and etc.
for your convenience,i'll add the links here:
http://www.aniosoft.com
iPod /iTouch/iPhone transfer to PC

Okay what you have to do is quite simple.

Just perform a backup of your iPod using CopyTrans (http://www.copytrans.net).

Then manage your iPod with this free iTunes alternative:

http://www.copytrans.net/m

Hope that helps!

I was struggling with the same issue and after browsing through numerous forums and sites. I finally found the solution in Sharepod.

It is an opensource app that directly opens the iPhone up and allows users to directly add, remove and even copy to PC their Music.

www.getsharepod.com/

Hope this helps.