Two things to prevent marring the laminate.
1. Use a finishing blade, not a rip blade (the finishing blade with have many more, smaller teeth than the rip blade (They’re pretty clearly marked on the packaging regardless)
2. Place a strip of masking tape along the cut line on both sides of the board.
As far as the side panels go, are they actually curved or just angled? If angled, then just use a circular saw and guide, or make a simple guide jig for the table saw. If curved, the proper way to do it would be with a router and a jig. But you’d really need a CNC router-cut jig in the first place, which obviously isn’t going to just materialize out of thin air. I would probably trace the curve onto the new board, make rough cuts with a handheld jigsaw (skillsaw), and then go back with a sander to get the finished edge. Finally you’ll want to cut a channel for the edge trim with a router, and then place the trim. Sort of a lot of work versus just getting close enough by cutting a straight angle. Just depends on how closely you want them to match.