If I'm reading correctly, you are not playing, but faking playing a keyboard. So, just get the cheapest keyboard you can find, a garage sale Casio keyboard will be fine. Then get a Ketron Midjay. It will do all you ask and more.
My REAL opinion is that you should do away with the keyboard, be honest and just stand up and sing along with the background. I'll bet you're not fooling as many people as you think.
DonM