I think it would just be a case of adding as much mass as is practical. Too much and it will just be in the way and too little and the gun will be shooting the bottom dwellers. But the more mass you give it the better the gun will behave when fired. I should think off the top of my head something like 25mm thick 15mm wide at the front and 25mm wide at the butt should do it and of course with that added wood goes some added lead to balance/ballast it. Do you have access to a pool you could take your gun into in Cairo? If so then try sticking on some cheap softwood with double sided tape to test out the "swingability" with some strips.
The formula for determining the recoil is:
[Mass(shaft) * Velocity(shaft)] / Mass(gun) = Recoil(gun)
The smaller the Recoil of the gun the better but it will never be zero.
If you're doing this keep us posted, I'm keen as hell to know how you get on
