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There are also router jigs for the Dremel that sometimes make it easier to use. I think RotoTool and ZipTool are also brand names for small routers for this type of job.
If you can't get the old laminate/veneer off, it may help to buy some heavy kraft paper (sold in hardware stores, roofing paper, flooring paper, etc.) and lightly tack it in place. Mark it, then lay it down flat and trim it until it has the right shape, going abck and forth in position. Once the shape is right, you've got a template to work on flat laminate with.
If you can make a heavy paper template for the whole panel, and then transfer that to the laminate, you may be able to get away with only needing the final sanding once it is glued up.