Technically if you are celebrating a birthday then you may ask for a birthday button. Disney doesn't ask for proof that it is a birthday. For instance we were in Disney a week after my birthday a few years ago, but the trip was specifically my "birthday trip" so I wore my birthday button proudly the entire week.
You will have lots of people--CM's and guests, saying Happy Birthday to you while you wear the button. As long as you are comfortable with that then go for it!