I'm finally done stripping and patching up the cabinet. The trim turned out to be harder to reproduce than I had figured.
Initially, I tried to cut pieces out in a continuous zig-zag using a utility knife, veneer saw and dremel tool. I had trouble keeping it uniform and had some breakage.
So, I changed tactics and cut out small segments instead. All it takes is scoring the veneer with a sharp utility knife and pieces can be snapped off.
Then, I carefully glued it down on the cabinet.
I can finally start putting on the new finish