Need suggestions on how I should cut and router this so not to mess up the laminate
Router or dremel would be the "cleanest" cutters. But you could use circular saw, or maybe a jigsaw.
If you use a circular saw, try to find a "finishing" blade with as many teeth as possible. Place the board so the laminate in on the opposite side as the saw: upside down with a hand circular saw, upside up on a table saw. Don't rush the cut by pushing too hard.
If you use a jigsaw, get a fine tooth wood blade and set the jig to "smooth cut",
not "orbital cut". Again put the laminate on the opposite side than the saw: upside down. And again, don't push too hard.
If you're really worried about chipping and don't have a router, you could clamp a piece of wood on the laminate side on the cut. (The wood will get cut too.) Or even score the laminate before cutting.
With a router, you can rough cut to about 1/8" to 1/4" (the rougher the cut the farther away you'll need to be) from the final edge you want and finish with the router.