As the contractor, API 1104 makes no reference to your responsibility to inspect welds.
Section 8.1 (of the 19th edition) allows the owner the right to inspect as much as they want.
Another thing to consider is the responsibility of the Pipeline owner. In the US, pipeline safety is the responsibility of DOT. DOT (by the 2001 Pipeline Safety Act) put 100% of the responsibility for safety on the owners. All "covered activities" (those that may have any impact on safety) must be performed by qualified personnel. DOT allows the owner to establish training, assessment and certification standards for those covered activities. In practice, the DOT representative who visits a site or reviews the program, will make recommendations for change if he/she feels they are needed (in short there is some subjectivity in this program).
I'm carrying on about all that just to make this point, the owner should be consulted for guidance in this matter. The API projects we have worked on have all been handled the same way: The owner inspects 100% of the welding. Knowing that, we assign our own CWI to look all of our work over before the owner gets there.
Charles