Most wireless charger pads have some sort of magnets to assist in affixing and securing compatible phones, so they could do the same amount of damage as any similarly-powerful magnets on any vulnerable mechanical watch.
But wireless chargers don't start unless they sync up with compatible phones and/or other devices. So unless you're charging a device and also have the watch at a very close distance I doubt the charging would contribute to any ill effects.
Just keep your piece away from the magnetic pad/cup and you should be fine. Use common sense and I doubt you'll damage your watch.
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