If there is no repair scheme covering a weld or stop drilling in the manual, but cracks are allowable to a stated limit (and quantity?), then I would raise a DD with reference to the AMM for the crack/s being there and for a re-inspection for propagation and additional cracks every Transit/Daily/Hours/Calendar with the overall time limit being to the cracks reach limit and/or next maint opportunity where exhaust can be replaced.
Alternatively, the operators engineering department could approve a stop drill temp repair (if they have the necessary approval scope), or approach the manufacturers for a temp repair scheme, which a DD could be raised against with the necessary requirements and limits stated in the repair scheme.
If the crack/s have reached the stated limit and/or quantity and no repair scheme available..........replace the exhaust before next flight.