I also think, if you must, cut your hair now and dye it after the wedding. Putting aside the fact it is YOUR hair or any of the negatives attached to this particular situation, you are going to be participating in someone's wedding, never mind that it's your sister's wedding. Take the high road and wait to color your hair until after the wedding.
While your sister may not have the right to dictate what you do with your own hair, is this really a hill worth dying on? As others have pointed out, it's been five years so another eight weeks is minor. As you have pointed out, you don't know how the dye will take so why not wait until after the wedding? To me, it wouldn't be worth the possible fallout. Yes, your sister is not happy, but, "guilt-tripping" tone aside, she did ultimately say it's up to you. However, was she supposed to lie and act like she was okay with it? When I know my feelings about something make me a bit of an SS, I will tell DH this and tell him I know I'm out of line and that the decision is ultimately his but that, honestly, I know I won't be happy about it. Your sister is telling you what she knows is the right thing -- it's your hair so it's up to you. Granted -- she probably should've been upfront and said what she was feeling, instead of using a guilt-tripping tone, that she wouldn't be happy with you coloring your hair. However, it sounds like there have already been so many problems between you regarding her wedding that it wasn't worth addressing directly (and, I know, I just wouldn't want to deal with discussing it further but would be unable to leave the emotion out of my voice).
For me, I wouldn't think it worth it if I were you. Two months more to make the dramatic change I'm gifting myself for the sake of letting someone else's special day be more important? Sure, why not? In the end, I'll know I took the high road and that there shouldn't be any fallout resulting from my actions because I chose to go this way (and I've recently taken the high road a few times lately when I've wanted very much to go in the other direction).
In this situation -- your hair, your choice but so not worth it to me knowing the bride's not thrilled about it.