Personally, I wouldn't worry about the songs that are on it.
Even if anyone else could read and even make copies of those files, there will not be any specific information in them that you need to be concerned about. The reason for wiping an iPod prior to selling it or giving it away (as recommended by Apple) is two-fold:
- a seller is not permitted to sell or give away copies of music that they have purchased as this would be an infringement of copyright laws. However, if the iPod cannot be wiped due to a defect, it would be unreasonable to expect the seller to delete the music. But if it's broken, the buyer (or recipient) would not be able to make use of the music anyway
- certain models of iPod, such as the iPod Touch can (and therefore may) contain information of a personal nature, such as saved passwords to certain accounts, including the seller's Apple account, bank account, email and notes containing personal information etc. This sort of information is not held on an iPod Classic
If you have any concerns at all about anyone having access to your accounts via an old iPod, change the passwords for those accounts on your new devices. That would lock the old device out of the account.