In the normal standards which I reference there is very little data for material this thin. AWS Standard C1.1 has set up data for Stainless Steel at 0.38 mm (0.015 in) thick but no testing information of the welds.
Further discussion with colleagues revealed that anything below 0.2 mm (0.008 in) is considered foil per AWS Standard D17.2 (An Aircraft Specification). Below is the table of contents for this standard AWS D17.2. It may offer some insight to this inquiry?
If the end user has not supplied a specification, then consider calling the weld either Class B or Class C and evaluate accordingly.
Reference: AWS C1.1, Recommended Practices for Resistance Welding
AWS D17.2, Specification for Resistance Welding for Aerospace Applications