Brian your questions were: "How deep of scratches can be removed with a sander? I have some scratches that may be 1/16" deep. I don't want to have a divit from sanding. I am going to try and design around the scratches if possible.
Someone else had asked about cutting a Corian countertop recently. The recommendations were a router with a straight carbide blade and a bearing that would run across a straight edge glued to the bottom."
1/16" can be removed but you have to go far beyong the scratch to "feather" in the repair. You didn't mention what color Corian you can get. The more profuse the pattern the easier it is to repair, because the seams and joints just dissappear. Regardless of the color, If you have enough, then design around the scratches.
Corian can be cut with a router. The typical cutting tip is a straight in "plunge " type blade. There is no bearing on the bottom, (that type of tip is used for laminate only) your guide is the round edge of the router base. That runs along a straight edge properly spaced from your cut line. But the saw is a quicker way.(And easier)
Take advantage of Ron The Bus Nut's offer. He has adhesive and scrap pieces. He ships very quickly and is a very good resource.
If you would like to see more work that I have done you can go to: www.cruiser-magazine.com
click on the picture of our bus (the '48 Marine Corps green Silversides) and that will take you to many, many pages of how I did stuff. (OK, OK I know I need to add new pictures, 'cause I've done a lot more.) But there is a lot there to see. You can also reach me off board at: davesiegeldesignsATgmail.com (change the AT to @).
It is also not unrealistic to consider mounting that "drop-in" sink as an "under-mount sink" I can show you how, and your wife will love you to pieces. (Once you take the trouble and actually use an undermount sink, you will understand what I am talking about.)