I have two Apple Watches can I turn off sleep / wake up on just one?

I have two watches one Series 4 the other is a new Series 10.

I keep my old watch to wear during the work day in my harsh physical job to save my new watch getting scratched at work.

My new watch I wear only after work, in bed, to monitor heart rate and sleep, and all weekend.

I use alarms to wake up the same time every day for work. However unless I especially ‘skip for tonight’ every night on my old watch it alarms in the morning in addition to my Series 10 which I am wearing, when I want it to ‘alarm’ only on my new watch.

So if I decide to snooze on my worn new watch the old watch carrys on alarming to wake me. I just want it to be quiet and not alarm as all as I wish to have this on just my new watch

Can I turn this function off only on my old watch always?