Save an edited file in nano, but no permissions

Yes you could save it temporarily to your home directory. Press Ctrl+O to change the path to your home directory or in /tmp and then press Enter to save it. Then you can sudo mv it.

Press CTRL+O will show you the path. Change that to your home directory or /tmp. For example File Name to Write: /tmp/filename and press Enter.

Just open a new tab in terminal, use chmod to change permissions of the file to 777, save the file in nano, then change the permissions back to what they were, probably 644. An alternative is to change owner using chown to yourself, save the file, and change ownership back to root.

Try ctrl+o and choose to save the file to your home folder.

Then do sudo mv /home/username/file /etc/