I would recommend the use of workmanship samples.
Commercial welding standards may not give you what you are looking for because most are concerned with the structural integrity of the weld rather than the appearance. Were I forced into a corner and if I had to specify a welding standard for your application, I would opt for D17.1 (an AWS welding standard for aerospace applications), Class A welds. They would most likely meet your expectations for cosmetically pleasing welds and still meet integrity requirement. However, the project specification should clearly state that while the visual criteria of a Class A weld must be met, additional NDT is not required if the welds are not intended to carry applied loads. Class C welds can be specified for those welds that do not need to meet stringent cosmetic requirements.
Still, workmanship samples are something that the fabricator, welder, and inspector can see and touch. Nothing is better than a physical specimen that can be used for comparison and evaluation.
Best regards - Al