This is no easy thing that you're dealing with, but whatever you decide to do, it's not a good idea to go behind your son's back.
Down the road, my biggest concern would be that GF becomes an unfit mother, your son wants custody, she gets the DNA test, real father lays claim and your son loses GS altogether. If by then, the child is old enough to realize what's going on, the worse it will be for everyone.
So, it's better to know the truth now, not later. Talk to your son about a paternity test....it's a good idea (for peace of mind, if nothing else) but the matter is a very delicate one.
I can't tell you how to go about this, except to approach your son when he's alone and in the right frame of mind. Choose your words very carefully and remember that timing is everything.