I did the same thing with a Corian clone (Hanex) a few years ago. This material is surprisingly brittle. To re-use the fiddles I very carefully drilled and tapped for machine screws to replace the sheet metal screws used to hold the fiddles into the old plywood. The force of turning in a sheet metal screw could easily crack the Corian. I ran tests on scrap material before coming to this conclusion. Also, if the fiddles were drilled to go into the plywood at half the thickness you will find that new holes will be too close the the bottom edge of the Corian. I plugged the old holes and positioned new holes at half the thickness of the Corian. Drill and tap very slowly - the material is too expensive and too time consuming to work to ruin it.

In my case the fiddles were rabbeted deep enough to cover a 1/2 inch ply with the 12MM Hanex on top. Three quarter inch ply with Formica on top is about 7/8 inch thick. My fiddles stick up 1-1/2 inches.