"Non-destructive" has to be a little flexible here. It's never going to look the same and there is a strong risk of sinking your knife into the circuit board (or you palm).
You cut round the bonded seam to remove the dished back. You have to go quite deep along the lower third of the sides because there are chunky bits running along inside there. I found the top edge (where the strap attaches) a bit easier.
Putting it back together is more straight forward. 2-3 rubber bands do the job nicely, though the whole case becomes a bit squishy once its integrity is compromised. A zip tie round the neck holds the strap better than the original rod and slot arrangement (in my view). None of it is very elegant though.
I haven't tried re-gluing primarily because none of my attempts at repair have proved satisfactory. I can make it a little better or worse but it always goes wonky after 20 minutes or less. There's a dodgy connection, but who knows where. I don't fancy your chances either. Unless you find such activity entertaining I'd just pass it on to someone who does.
The whole exercise has given me greater insight and respect for the overall mechanical design so I'm glad I did it, but it was mostly frustrating.