Well I guess it's a good thing you haven't submitted it yet. Even if you had already submitted it, some schools have you list your ECs (again), as well as any relevant awards you might have received. For example, MSU is not only a paper application and a big one at that, but their secondary asks for all the ECs you listed and Awards, etc. I believe it even asks about High School stuff? I can't remember now, this past application cycle has turned into one big blur.
What I would do is just leave it on your primary, but add the contact info for the dept who granted the award (name, address, telephone number, fax number). The logic here being that an applicant wouldn't want to lie about an award AND give the contact info which might unravel the lie should a school call up the dept to inquire about the legitimacy of the award you claimed to have received. You follow?
Your other option would be to go ahead and send the award letter to each school. I just don't think it's necessary if you put the contact info. It would also be an added expense in sending an additional document.