No pressure!
There is a lot that a guy can do to improve the aesthetics of the GPR and removing a little of the perch belly is one of them. But as has been mentioned, it will bring you to other issues, kind of like painting only one room in your house.
As you shave away the bulbous perch belly, the wood of the butt stock grows thicker moving toward the cheek piece. This will show as the two lines along the flat bottom of the stock diverging away from each other, and then converging toward the trigger area. I order to improve that perhaps unforseen feature, you will have to rework the entire butt stock on both sides to make those two bottom lines parallel again. This is not a bad thing, but adds to the work required to 'make it right'.
One of the architectural features of the GPR that benefits greatly from attention, is the standing breech and the top of the wrist. the tang itself has two bevels ground or cast into it - don't know what that's for, but they are buried in the wood in that big hump behind the breech. The tang needs to be bend down a bit directly behind the vertical 'break off' and then some of the curve removed from the arc of the tang. Once this is done, the tang is re-inlet a little deeper and the wood and the steel filed together to eliminate the bevels and remove the pregnant hump. When this is done nicely, together with removing most of the perch belly, the lines of the butt stock suddenly take on a much more pleasing form.
The stock of the GPR is created from the factory by 'slack-sanding' which avoids the necessity of the manufacturer to employ hand work for finishing. But slack sanding cannot get into the radii that will make the cheep piece side a lot nicer. So a lot of wood has to come off the cheek piece side especially, including the cheek piece itself which, from the factory is very voluptuous. If it would be useful, I will see if I can find some of the images I took of Brian's GPR re-build, and post them here.
To better answer your question, you will use a plane, aggressive rasps like Nicholson's 49, and various files, ending with abrasive paper or cloth backed by various shaped pieces of wood and rubber. The GPR wood that I have worked is some form of European walnut, and is extremely hard, so it will be nice to work with and take a fine finish. If you choose to do the work, and are patient and know where you're going, the result will be remarkable, and you will enjoy your rifle that much more for having customized it and removed the factory ... looking for the right word.
