Hi Mike, the corrector plate is hard as. Don't be scared to handle it and wipe it good. You can't hurt it.
The Primary Mirror, well if it's reasonably clean leave it alone. It's no drama to clean it but it's fiddly. Greased baffle tube, cork spacer, etc... It's not like a dobs or newt where it's easy to strip everything of it then give it a bath. If there's anything that bothers you on the primary get a cotton butt with a bit of acetone on the tip and get the stuff off. Leave it in place.
Secondary is a no brainer: take it off if you want and wash it.
What ever you do take a pic of the corrector plate so you know where your shims are. Also there should be a line on the edge of the corrector at 3 o'clock facing the scope, so opposite to the focuser for the orientation.
AND you should have a line at the back of your secondary that point to the same spot at 3 o'clock.
Finally there also should be a mark on the edge of the corrector like a ">" that shows you which side of the corrector goes inside the scope and which face is out.
Have fun.
PS: and while you're at it flock your tube.