Do I wish my ex a happy birthday?

My ex and I broke up nearly a year ago and since our break up we have not spoken a single word to each other. Our breakup was definitely not the smoothest and it broke my heart especially because he was my first boyfriend and my first time feeling in love. I got a reminder from my calendar that it’s his birthday tomorrow and I’m debating whether sending a quick “Happy Birthday Hope all is well” text would be a good idea or not. I do wish him well and I no longer have anger towards the guy, but would it give the impression of desperation or being small if I do message him?