Is there a way to completely erase an iPod Nano 3rd generation without installing iTunes?
The iPod nano and classic iPods get loaded a custom firmware that could be downloaded from the internet and possibly loaded with a tool other than iTunes, but on a PC you could easily use whatever disk tool you want to erase the drive by reformatting it.

Since this would render the device unbootable, you will not want to sell it to a user that's not familiar with why it's not working, so the elegant solution would be to rent another computer with iTunes and restore it.

Apple's retail stores usually will even loan you a cable to restore your device from any of the display Macs. iTunes on a new computer would want to erase all the content anyhow - so going another step to wipe and restore the device will leave a clean slate and you might even be able to sync some demo content to the device depending on how iTunes is set up in the store you visit.