If you really want to get picky, you are better off leaving the battery connected instead of unhooking it and leaving the cables floating. With the battery connected it limits the DC voltage you can subject the system to. Otherwise, if you're not careful with the ground clamp placement you can get the full welder voltage between ground and a power wire which will fry things.
For example, the Ford EEC-IV ECUs had poorly designed voltage regulators and they would fry if you subjected them to too high of an input voltage. Had one fry when someone unhooked the battery to check if the alternator was good (don't do that on any computer controlled vehicle, btw).
Either pull both cables and connect them together, or just be smart and make sure your welder ground is close to where you're welding. Don't be stupid and put the ground clamp on the bumper and start welding on the exhaust.
All those muffler shops can't all be wrong. :} Lazy maybe, but they are greedy and generally avoid causing expensive damage when installing a $49.99 muffler.