How safe is it to provide my credit card information to an admissions office?
I wouldn't send any personal information like that through an email, even if I were sure the email was sent from a secure and trusted location. Whether this be for an admissions office or anywhere else.

My advice would be, if you wanted it, to call the admissions office directly and provide the information over the phone to get the express service. There is an added fail-safe of you looking up the number and calling it yourself to ensure it is legitimate. 

Otherwise, just take the free postage if you are that concerned about having your details stolen.