Thanks for reposting those photos. I believe several folks have successfully shortened the muffler by cutting it like that, and it does make it look a whole lot better. Reports I read indicated it didn't change the sound, just made it smaller so it didn't stick out the back end so far.
The weld under the rear cap has to be ground off so the muffler core can then be pulled out of the outer casing. The section that gets cut off is the flame arrestor section off the FRONT end of the muffler core, and then the same length has to be cut off the REAR section of the outer casing, being careful to match the original cut angle, and the muffler internal core is then slid back in the outer casing and it has to be TIG welded back together at the rear when you're done.