I think the sticky back is the paint dissolving from finger sweat and maybe aging.
This seems to be a common issue - if you look for used 9600/9800s they often show some wear on the back plate.
I think there's nothing that can be done by cleaning.
The only solution I see is to remove the back plate, use some fine sandpaper to remove the paint completely and repaint the whole thing.

I did that once for one of my 9800s, but unfortunately it already shows some spots where the paint did not stick (despite of using a primer before spray-painting).
So it's probably a good idea to get an opinion on what paint/primer to use from someone experienced in painting plastic pieces.

Sebastian