iPhone backplate mod: On what side of the iPhone 4S backplate should I paint?
Try painting the glass with paint, not just the bursts, but the whole plate on the outside.
Let the paint dry and then scratch the surface clean with a hard plastic object (so you don't scratch the glass).
Normally the paint will have dried in the bursts and you shouldn't be able to scratch off the paint (while the paint on the glass will be scratched off).

About the electronics; if you use normal paint, it won't harm the electronics.  

But why don't buy a new cover on eBay for just $9? You can simply fix this yourself within 2 minutes!