First of all - congratulations. Remember, this is your day and you are the most important person.
People like to muscle in and try and get a bit of the action when someone is getting married - I'll bet you have had all sorts of people offering to lend you stuff or do something for you. It's called reflected glory.
However, you will never get a chance to shine like this ever again so be a little bit selfish.
If you don't want to hurt her feelings, say you have decided that you would rather wear flowers than a tiara, or that your head must be much bigger than hers as you wore the tiara round the house for half and hour and it gave you a headache or that you are wearing a family one that your fiancee's mother has produced or something like that.
Please remember, this is your day, not your friend's, who has already had her day in the limelight. It is the one chance you will get to behave like a princess, so just go ahead and do it. If she is any kind of friend, she will understand: if she does not understand, do you want to keep her as a friend?
Have a great day and don't let yourself get stressed out by too many situations like this beforehand - you will find this is the first in a long line of irritations (like writing thank you letters for the presents, trying to get Aunt Mabel to the right seat, bridesmaids being sick, mother's hat etc.). Keep smiling and breathe deeply.