I'd be wary, especially if you're applying to some of the same programs. A prof once instructed my class to bring in a revision we were working on, and I selected a dramatically revised short story from my CW sample. The protagonist went from being a young woman to an old woman, the tone went from serious to light and humorous and the entire plot had changed. My prof still recognized it as being from my CW sample (not that that was a bad thing given that she asked for a revision--I was just surprised by her memory), so there's a chance the admissions committees might recognize yours and it all ends up the same way.
I know time is hard to come by, but ideally, you should be writing and revising as much as you can (especially if being a writer is a long-term goal of yours). It's highly possible you'll create something even better than the story you treasure (hold onto it!--just maybe not for this). The applicant pool changes every year, so there's always a chance an admissions committees could privilege a portfolio of yours containing this partciular story over other applicants this year, but I think you significantly improve your chances if you try to deliver different and even better the next go around. And if you're starting to work on your applications this early in the game, you've got plenty of time to bring some work to life before most CW programs' deadlines.
