You can't directly move your music from the iPod Special Edition to an iPod Nano. You will need to use iTunes as a go-between. So basically, transfer (sync) your iPod music with your computer's iTunes Library then turn around and sync your iTunes Library to your iPod Nano. Music transferred.
Please note that any music acquired from the Apple Music Service requires an internet connection to access, so iTunes won't transfer any music acquired from that service to a device incapable of establishing an internet connection remotely. Since you are talking about music you converted from vinyl, this shouldn't be an issue for you.
Sync your iPhone, iPad, or iPod touch with iTunes using USB - Apple Support
If iTunes doesn't recognize your iPhone, iPad, or iPod - Apple Support