Opening up the exhaust can possibly mess up the fuel tables. But the thing is how much it changes it depends on a lot of other stuff. If the cat and exhaust system all the way to the back of the car is stock then you swap out mufflers it might only change your fuel table a tiny almost unnoticeable amount. If the rest of the exhaust has been changed and you are now replacing the stock muffler with a different one it can have a larger impact. There is really not a lot of ways to predict how an exhaust will change things other than trial and error.
For economy type driving the flow really doesn't matter so it would be possible to put some reducers in the pipe before the muffler to choke it down to 1-1/4 then run a few inches at that size then go back to 2" to a bullet type muffler. That would help keep the low speed exhaust working well but would hurt the top end.
If you want to make it sound strange get a sweet thunder one chamber muffler
It will take away all the higher pitched sounds and leave only the lower sounds. Nobody will have any idea what type of engine it is when they hear it run.