Yeah, there's no time zone in the game, just the time you've set on your Switch and you can change that easily.
I don't think it would cause issues. At most you'd be skipping a day depending on the hours and that's hardly a big deal. You're just moving to Europe, though, so I don't see a problem. I live in Europe and when I'm playing at night I regularly set the clock to morning or afternoon so stuff will be open and it's never been an issue when I go back to normal time.