Deaf people have a vibrating pad under their bedsheet.

If you always go to bed at the same time you should wake up at the same time. Do you have an irregular schedule?

I haven't needed an alarm in many years, but when my sleep cycle was poor I always needed it.

If your wife is the type who would want to wear a sleep mask, you could put your lights on a timer to make you up, if you have smart lights a lot of them have a feature to turn the brightness up slowly to wake you up more gently. She wouldn't be bothered by them if she's wearing a mask but they'd get you up.

Hatch alarm clock uses light to wake you up. There are cheaper knockoffs on Amazon.

There are these lamps that mimic natural sunrise. If you put one on your side of the bed and sleep towards it, might work. I used one a decade ago and it worked ok. Keep the watch alarm as back up though

If you can wear sleep headphones the Sleep app for android will send it's alarm to headphones. And it will ramp up the volume of the alarm over time. I imagine there's something similar on iOS. I wear SleepPhones... they're fine.

You can try the watch again with very low volume or some quiet alarm sound with no vibrate and leave it under your pillow.

I got a sunrise alarm clock recently and I've really been enjoying it. Whether it will work for your situation or not depends on how sensitive you each are to light in the mornings.

Set alarm quiet-ish on your phone, put it under your pillow then hope the volume is loud enough to wake you, but the muffled sound doesn't wake them up?

Try gentle, natural sounds in your alarm. Bird songs, sound if rain, etc. Many alarm apps have an option to start very quiet and increase volume gradually, that may help

I have no idea if this is a good product or not but look up shock clock alarm watch. It uses an electric shock to wake the wearer up.