I do this kind of thing all the time. I use my Festool rail saw for dust free cutting, but it will only reach to within about 5" of the wall. Draw a fine pencil line from the cut to the wall, and using a Rotozip, cut right next to the line without touching it. You may like having someone hold a shop vac to suck up the chips so you can see what you're doing. Make a few passes; breaking a bit off inside the Corian stinks, believe me. And don't tip the bit; stay as perpendicular as possible.
Once you're through and the piece is removed, use a belt sander or sanding block to make the freehanded part flush with the cut. You can even kiss it with the Rotozip again. Rip a piece of edging off your drop, tint some epoxy for color match and clamp it in place, sand the squeeze-out to flush and profile the edge as appropriate.
I had to do this on this job this week:
In the picture above, notice the front edge has been ripped off before the ledge. That's because the front edge must be glued back on the main edge. Usually you build up an edge from underneath, but in this case I can't profile the edge (without removing the sink top) because my router base will be stopped short by the wall.
The solution is to adhere the already-profiled edge.
The splash was cut freehand with a Rotozip the same as the last 6" or so of the top using the method above. If you look really closely at the top where the splash ends, you may be able to see an adhesive line.
Q
Julien signature sinks model 253
Q