Is there any way to change the wrist side (from left to right or vice versa)?

No option found - it used to be there.

It's still there for me.  This is on version 4.38.0.31 of the Garmin Connect for iOs app.

I have the same version.  Tap on your device, not the more icon, then “general”, it will show Wrist Worn On in that screen.

I don't have that option either or cant seem to find it. I do remember it being under "general" settings like mentioned previously. :/

It's still available on my app.  If it's not on yours try contacting Garmin support to see if they can help you with it.  

It is no longer visible on mine either - it used to be but it's gone...

In my case it is like this:

- tap on the device icon - for me it is a Garmin Vivosmart 4

- tap on "General" menu item - has the jagged wheel icon typical for settings

- tap on "Wrist Worn On"

Any luck figuring it out? I’m having the same problem.