Can I turn on a Sleep alarm ONLY on Apple Watch and NOT my iPhone?

I normally charge my phone outside my room, and only wear my watch to bed. Therefore, it's the latter that wakes me up. But it SERIOUSLY infuriates me when the phone outside rings too, and EXTREMELY loudly, waking every family member up. I then have to quickly rush out of bed, half-asleep, out the door, and all the way to the place my phone is charging, just to stop that alarm. I know you can set any alarm on the phone but not on the watch, but I want the opposite: is there a way to permanently set a Sleep alarm ONLY on my watch and leave it off on my phone? Plus, the standard Alarms app doesn't count: I want to be awakened to gentle music, not beeping.