Based on my own recent experience, I might suggest that you stop fighting this and stop thinking of it as all that annoying.
The group singing of Christmas carols has a charm, and you don't have to sing to enjoy it. So find some way in which you could enjoy that half-hour, and try to exercise that. Either stand around listening to everyone else--don't even bother to lip sync, just listen. Or sit on the sofa and be the audience.
And then say that--if you indicate to Aunt that you're participating in some way, instead of looking as though you're rejecting everything about it, she won't be quite as tempted to badger you. "Aunt, singing is not my thing, so I'm going to sit here and enjoy watching and listening to you all. Every Christmas caroler needs an audience, right?"
When people badger you, that's the time for the absolute cut-and-paste. Same exact words. Because it underlines the idea that you have given them an answer, and there is only one.
And if that doesn't work, then say, "Aunt, singing is not my thing. Please respect that."
You really can be pleasant and not participate without making a rude big deal out of it. . . . It's a hour or more out of your life if you hate it. It's only an hour out of your life if you just want to go along but stay in the background.
Luci45 has a point.
Also, from my own recent experience--all the stewing you do when you're NOT caroling needs to be counted, too. (This post, and all the times you check it, should count. Add them up--you'll be surprised.) If you drop the stewing, and resenting, it'll be only an hour.
One other point: all traditions start somewhere.
I'm also likening this to my late-in-life "acquiring a taste" for coffee. I first tried it black. Couldn't stand it (but loved the smell). Recently I tried the International Coffees from Nestle, which have a lot of dry milk and sugar. Liked them! Not an easy or automatic thing to like, still. But it gave me a transition in. Probably in a couple of years I'll use less sugar--I can tell that this will come.