ttyrec allows you to record your terminal sessions easily. However, they are recorded in a special format (not video), but the resulting files are smaller, and as such easily transferable.
I use playterm.org as a hosting for my ttyrec files. It allows you to view your terminal recordings over a browser (as if it were a video).
Steps
Recording
sudo apt-get install ttyrec
ttyrec
#Type your commands
git init #Example command
exit
A ttyrec session is similar to a screen session, except that it is recorded. After your recording is complete, a file with .tty extension will be present in your directory. You can upload that file to playterm, or pass people a download link.
Playing
To play the file, they'd need to use the ttyplay command. Just use ttyplay file.tty and it should play your terminal.
Editing
Since you are comfortable with adding audio later, I'd recommend copying the ttyrec file to a normal ubuntu desktop, and playing the recording (using ttyplay) while recording it using a screencasting session. You can record your voiceovers at the same time.
References: