Ooooh, I don't like the idea of having a whole accompaniment in your ear that only you can hear. It's bound to make the song sound a bit strange and stilted. Most unaccompanied singers bend the rhythm slightly in order to enhance the melody or the words in various ways - you'd lose that, and instead you'd have silent bars between verses and sections that your listeners couldn't hear.

I'd advise getting away from all electronic devices when performing to others. Particularly if you're doing funny parodies, there's nothing worse than someone reading it out from a script (well, there is something worse, and that's singing a humorous song with your eyes closed, which I can tell you is very disconcerting for the audience. But that's a whole nother issue). You sound as if you've got the right idea, just learn your songs, trust yourself and go for it!
Marje