To be honest, I doubt your guests are THAT bothered about it at this stage - off the top of my head, I can remember being at 2 weddings where the bride was pretty late (I can't remember exactly how many minutes, but I'd be fairly confident that it was half an hour anyway) and while maybe people who aren't that close to the bride (i.e. don't know her very well) might have been grumpy about it, most people assumed that something had gone wrong to cause the delay and nobody minded much once she arrived and it all got underway.
For you, you're bound to feel it far more intensely than anyone else, because you're SO much in the spotlight on the day anyway, you're the one who thought about this day for 2 years or however long, and as a normal human, you're the one who's always going to be your own biggest critic in any situation, so from an outsider's point of view, I don't think you need to keep stressing about it and I definitely don't think you need to write an apology to people in the Thank You cards unless you feel that it would alleviate your stress over it. Do whatever you think you need to do to let yourself off the hook but please forgive yourself - I can promise you that your wedding day was only dissected in minute detail by YOU, not by any of your guests, who just attended another wedding, same as any other (sorry if that sounds mean but it's the truth!! Everyone else goes to a wedding, enjoys it, reflects on it a little bit for a day or two afterwards and then forgets all about it while the bride spends ages thinking back and obsessing if things were ok or not!)