@Rickster, your location of cutting (all around) is not a bad one, but consider that, there are several u-shaped pipes in it, which are loose and cause this rattling noise.
Once removed it will be pretty noisy and might void your next technical inspection. Also NOx values will change (don't know requirements in your state).
IMO better to open sidewards, spotwelt this silencers again in its place and weld it close, smooth and paint nicely to have an original muffler again.