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This has been my exact experience (except with an Omega).

I also wear my real watch on my left hand, and AW on my right hand.

I Actually tried wearing an Apple Watch and mechanical watch a separate wrists and it actually it was not as uncomfortable as I thought it would be. I typically use Apple Watch for the fitness capabilities and then my mechanical watch for the actual time keeping. I Don’t do this all the time, but there a few times where I have worn both my Apple Watch and mechanical watch.
 
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