Realistically, your wife is your partner and some sacrifices need to be made. If she can't sleep through a watch, she should consider earplugs or just deal. I'm sure you silence it and leave the room ASAP so, that's just life of sharing a room with a spouse.
Edit like literally millions of spouses have tolerated their other rising before them, it's a normal part of the deal
My dad has had the single fucking loudest alarm clock for literally my entire life. It's such a god awful racket. It had to be, because my dad has the worst snoring I've heard in my life. Man sounds like a chainsaw, and you can hear him clear across the house. My mom would sleep directly through it all. It's wild.
Damn, I was coming here to say this. All I can add is that maybe sleep on your stomach with one of these, otherwise it could wake her up vibrating the mattress, since she sounds like a light sleeper.