If I were you, I think I would hold off on the hair change until after the wedding, but not because of anything to do with your sister.
I would wait, because it is a really drastic change and might not come out like you think it will. I am by no means saying that dying your hair, to whatever color that might be, is a bad idea. But sometimes these things don't come out as planned, especially if you've never done it before. It might take some tweaking or changing until you are really happy with it, and you might not have time before the wedding to finish this, and you might end up forever in wedding photos with hair you hate.
And to me, it still counts as celebrating your milestone birthday if you do it after the birthday. My opinion is that anytime within the year would count. I don't see it as a conflict between you being able to celebrate your birthday as you choose and your participation in the wedding, to be honest.
Right now, you know your hair and what it does and you can feel comfortable putting it up, knowing what will happen. It might feel boring but it is also predictable. And even if your sister didn't care if you dyed your hair, do you really want to spend the whole wedding distracted by people coming up to you and commenting on your hair, even if those comments are compliments? When I was in my sister's wedding, for example, there is no way I would have had time for all that, being very busy with other things.
I know it might feel like you are "giving in" to your sister's demands but I think there are honestly other reasons you might want to wait. And unless she's the type of person who will hold it over your head forever (telling everybody "she was going to dye her hair but didn't because I told her not to and she knows I am perfect and know everything" type stuff) then I would wait if I were you.