Yes, you can take them off. The place I bought my new panels from only sells the trim for 65-66 though. Fortunately mine were reusable. I'm sure you could find them somewhere, even if they are used or NOS. Good luck.
Standard or deluxe interior? If standard don't worry about them, your replacement panels will have the chromed plastic piping. If deluxe (about 0.8 inch wide metal edges) take them off and keep them, these are not reproduced yet (to my knowlege) and can cost quite a bit in good condition.