Track use loads an exhaust differently from the road. The system runs hotter for longer, expands more, and is worked by every kerb and every change of direction. The failures that strand a car are rarely dramatic: a clamp lets go, a hanger tears, a gasket blows out, a hose softens and slips off its bead.
So the kit should be built from the failure list rather than from a generic tool roll. Anything that has actually happened to you or to someone in the paddock belongs in the box; anything that only might happen can stay at home.
Carry spare clamps in the sizes the system uses, plus a couple of each type present on the car. A clamp is cheap to carry and impossible to improvise. Gaskets for the joints that get opened, and the fasteners for those joints, take almost no space.
Add the small items that stop a job: washers, nuts and a few bolts in the sizes used on the exhaust pipe joints and hangers. Take them from the sizes the car actually uses, checked at home rather than guessed in the paddock.
A broken hanger does not need a welder to get the car home. Lock wire or a metal band can carry a section temporarily if it is routed so it does not cut into the pipe or rub through something else. Carry enough to reach from the section to a solid point.
Include something to protect whatever the wire touches, and something to cut and tension it. A repair that holds the weight but wears a hole in a hose on the way home has simply moved the failure along the car.
Charge-air and coolant hoses fail by slipping, splitting or softening. A spare length of hose in the common size and a couple of good clamps cover most of it. Heat sleeve is worth carrying too, since a rubbed-through hose near a hot part is a recurring track failure.
Include the small service parts that go with them: clips, ties and a means of securing a sleeve in place. Loose heat material becomes a rattle first and a wear point afterwards.
A compact socket set matching the car's fasteners, a couple of spanners in the sizes the exhaust uses, pliers, cutters and a means of lifting the car safely matter more than a large kit. Add a light, gloves and something to lie on.
Whatever you carry, know how to use it on your own car before the event. A kit that has never been opened is a box of weight, and the paddock is a poor classroom.
Every item in the box is weight in a car that is already working hard, so the kit earns its place by covering a failure that ends a day. Clamps, wire, a spare hose and the tools to fit them meet that test. Duplicates of tools already kept in the car do not.
The rule: if losing it would end your session and you cannot buy it at the circuit, carry it. If it can be borrowed from the next pit or bought on the way home, leave it out and keep the box small enough to check in a minute.