Stop the bloody wine, woman!
Why are you so hung up on the fact he knows it was you? Why wouldn't it be you? You've already proved you're the person most likely to do it by - um, being the person that did it!
Who knows, exactly why. Maybe he mostly uses another email address these days. I changed mine 3 years ago - if something went to my old one now, I could pinpoint maybe 20 people that had that but wouldn't have new one. Then there's your writing. I can tell my XH in a single sentence because he always put a space before a comma, e.g. I am a wanker , a total wanker. 
As others have said - knowing both the birthdays and having any motivation to mention them puts you in a pool of suspects of... one?!
He knows it was you. He's in another sodding country, so it especially doesn't matter! He is the last person on earth that you need to care for the opinion of.
Don't sweat this.
Wine down, go get some air.
And imagine starting a thread in Chat next year "so what's the most cringeworthy post break up thing you ever did?" and reading far worse replies!