A system that is already built and already fitted is a different problem from a set of tubes on a bench. The mounts exist, the tunnel has been trimmed around the pipe, and the tip sits where the owner wants it. Shortening is a decision about which end gives way, not a question of how much metal can be taken out of the middle.
On most cars the work belongs at the rear section. That is where the longest straight run sits, where there are fewer sensors to disturb, and where the result is visible the moment the car comes down. It is also the end that can be removed and refitted without touching anything upstream.
The length that matters is the distance between two fixed points on the vehicle, and that can only be taken with the system hanging in its own mounts. Measure the section flat on the floor and the figure will be wrong by whatever the hangers hold and whatever the pipe has already settled into.
Support the system at its hangers, mark the tip against the bumper, and record the gap at the joint you intend to close. Two marks are enough: where the pipe sits now, and where it has to finish. Everything between them is arithmetic, and it is worth writing down rather than remembering.
A cut belongs on a straight length with something true on either side of it, so the new joint has a reference to align against. Cutting hard against a bend leaves a short curved stub that is awkward to hold, awkward to measure, and almost impossible to fettle once it is back under the car.
Wrap a band of tape around the circumference and cut to its edge rather than following a single pencil line. A cut that wanders around the tube will pull the run sideways when the joint closes, and no amount of weld will persuade the tip back to where the bumper expects it.
With the section out, the two ends have to meet in a way that does not load the mounts. Clamp the fixed side in position first and bring the loose end to it, never the reverse. The hangers should be carrying weight at that moment, not tension.
A clamp or a short internal sleeve will hold alignment while the tip and the clearances are checked. If the joint needs force to close, either the cut is in the wrong place or the face is not square, and welding it will freeze that error into the system for good.
A butt joint in thin stainless pulls as it cools, and a gap that has been closed tight has nowhere left to give. Expect the run to draw slightly towards the weld and the pipe to lift a little. That movement is predictable, which is why the joint is tacked in several places and checked before the seam is finished.
Material supplied as straight exhaust pipe makes this easier, because the wall is consistent around the circumference and the arc behaves the same all the way round. A consistent wall gives a consistent pull, and a joint that pulls evenly keeps the run where it was measured.
The first drive is part of the job rather than the end of it. Heat cycles settle the system into its hangers, and a joint that looked correct cold can show a shadow line or a small gap once everything has expanded and contracted a few times.
Recheck the tip position, the closest clearance and the tension in each hanger, then look at the seam again. Where the work is stainless, the technique in TIG stainless steel welding is what keeps the inside of the joint as clean as the outside, and that matters on a section expected to last.