I have no idea if this will be any use to you. I didn't even know the White Stripes song had been covered! So as you can see I'm way out of touch with the charts today.
However, I have written some stuff and it is all licensed as Creative Commons. Which basically means you can use it on You tube, perform it live without needing permission as long as you credit the writer and....important......... as long as you don't make any money. When money starts coming into play then discussions are required.
So for trying things out, try looking for stuff on-line a with a Creative Commons licence.The thing is here is that very few, if any, are professionals and if we were writing for you specifically is unlikely, but there my be some members stuff that you would like to sing. You'll just have to search and see. Some stuff I've written is available here.
http://soundcloud.com/mihkay. Probably none of it is to your liking but if anything catches your ear I can supply the lyrics and a vocal free version for you to play with. I'm sure others would be happy to do the same.
Good luck
Mihkay