"they are not yours anyway"
Nonsense. The songs may not be but copyright exists in a recorded performance, quite separately from the copyright (or lack of it if old and trad) in the words and tune of a song.

But you have a point about this being a demo.

I make a demo with incomplete songs - 1-2 minute extracts. That way nobody can steal them to sell. It's enough to tell an organiser, agent or recording label manager whether your sound is what they want.

Anahata