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.