I think it is better to discuss with your cousin/parents.
If your cousin is unable to change their date then you might have to change yours.
Think about this scenario, what if both your dates are the same, which wedding should your relatives attend?
Let's say you changed your wedding date, is the date 100 days before/after your cousin's? Is your parents/yourself pan tang? If any of you is then you won't be able to attend someone else's wedding 100 days before/after your own's.