Taking deep breath and holding nose....Here goes.
The crucial element in 'traditional' song is the passing on. No definitions actually state how many times something must be passed on before it qualifies which is where the grey woolly area comes in.
If you plump for the 'generation to generation' definitions, you then have to define a 'generation'. A 'generation' in this respect does not necessarily mean for instance parent to child, it can be as short as a season or a school year in the case of playground songs/games/rhymes etc.
Literally it could be you giving me your song you've just written, but I doubt if many here would accept that definition.

Why can't we just accept that some words don't have hard and fast boundaries carved in stone? I have to make my own boundaries on this regularly as I write about 'traditional song' on a daily basis, but I don't seek to impose my boundaries on anyone else. I can postulate on the origins and evolution of a particular song, but I rarely nowadays state that a song is or isn't traditional, I let the reader come to his/her own conclusion based on the descriptions I give.