The stock exhaust is plugged on the end with the smaller outlet not just for noise reduction but for back pressure as well. Remove the cap on the end and you lose the back pressure along with a loud engine similar to what you have now.
So now how is this pipe in it's current configuration give this engine any back pressure? You may find that after doing this silencer however way you may get overall better performance and longer life.
I'm feeling that exhaust was made for a 4 stroke.
Watch this animation on this link:
Two-stroke engine - Wikipedia, the free encyclopedia
When you watch that animation you find if you have no taper or restriction on the end you'll have no back pressure.
A 4 stroke doesn't need it so it can run open. But not on a 2 stroke.