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Thank you, @Gordon for your reply. Well, I'm not sure how loud sound I would get with such a small buzzer (if I could find one) in the middle of the watch fully surrounded by other components in a sealed case. I guess you are suggesting to attach a thin piezo, but I'm not sure how loud it would be without any amplifier which will take up space as well. Maybe I can put some SMD amp where the motor used to be.
Thanks again. If I make any progress, I will update this post.BTW, what's the thickness of the motor?
The hole is around 8.4mm but I don't fancy your chances. Even if you found one it's in the middle of the watch so is unlikely to make much noise.
All I could suggest is maybe you could epoxy a tiny one (10mm or so) to the rear of the watch and put the battery over it, but you might have to look at using a smaller/thinner battery to get the space for it.