You are partially correct in your thinking. I know that there is a way to preform Method #2 (below) on a Mac, but I don't have one so I don't know the exact steps. Here's what you should do. Transfer all of the music to another computer, like you said, except instead of using a flash drive (unless you have a huge flash drive) just delete everything on your iPod (will need iTunes for this) and then use it as a flash drive (just go to Start> My Computer> and double click iPod drive and drag and drop the music back into it). Although, Method #1 (below) is probably the most common way that Mac user transfer music. Plus, if you download 3rd party software you will have it for the future.
Transferring iTunes Music
Method #1:
Download Senuti or iDump or any other similar software from download.com (for free).
(The following steps are tailored for Windows XP. It will work for Vista as well but the steps may be slightly different. Also, this method does not require third party software or an internet connection. This method will transfer ALL songs from iPod to computer. Use Method #1 to transfer specific songs.)
Method #2:
>Connect iPod to computer.
>”Start.”
>”My Computer.”
>Double Click iPod icon.
>”Tools.”
>”Folder Options.”
>”View.”
>Select “Show Hidden Files & Folders” and click “OK.”
>Right click “iPod Control” folder.
>Select “Properties.”
>Unselect “Hidden” and click “OK.”
>A window will pop up. Select “Apply changes to this folder, subfolder and files” and click “OK.”
>Double click “iPod Control" folder.
>Double click “Music" folder.
>You will notice folders labeled “F00, F01, F02, F03, F04, etc.”
>Open up iTunes side by side with this window. Make sure that the “Music Library” is displayed and make sure that iPod/iTunes is set to "manually manage music."
>In iTunes select “Edit>Preferences>Advanced>and make sure that ‘Keep iTunes Music Folder Organized’ and ‘Copy files to iTunes Music folder when adding to Library’ are checked and click ‘OK.’” You should also make sure that your iPod/iTunes is set to “Manually Manage Songs” so that you have control over what you want to add or delete (to do this select the iPod icon under “Devices” on the left column of the screen and select “Manually Manage Music” under “Options.”).
>Drag all of the yellow folders (not the Read Me files) directly into iTunes “Music Library.” I’m talking about the part that has song name, artist, track number, etc.
>You will notice a progress bar indicating that the music is being transferred. Sometimes a message will pop up saying that a song is not compatible with iTunes and that it needs to convert it. Just click “OK” when this message appears.
>Note: If you have slower computer you may want to only drag a few folders at a time so that your computer doesn’t freeze up.