Yeah, I don't think there's a website that will do this for you, but if there were it would just be using one of the more popular projection systems to generate the results.
The most popular seems to be the CHONE Projection System (it's just a combination of 4 other projection systems...Zips, Pecota, Marcel, and Hardball Times). You can download the spreadsheet on BaseballProjection.com
and just cut and paste your team into a separate worksheet (like GotowarMissAgnes said).
It really wouldn't take very long to do.