Disclaimer, I'm not familiar with the wording in ASME B31.3. So, take the following with a grain of salt, since I don't know what 'outs' the spec has.
Otherwise, in general.... Typically you test that the service temperature, or colder. I never paid attention to the exact temperatures, but for NASA projects, Anything in a LH2 environment was tested at -423F and anything in LO2 was tested at -320F. If you want to get technical, we used liquid helium for the LH2 tests, and liquid nitrogen for the LO2 testing. I'm not not sure if we actually tested at those liquid's actual temps, or used them to get to the appropriate temp.
However, I would hope, that if this is a customer requirement, they gave you some guidance beyond ASME B31.3.
Whenever I worked on one of these the customer spec had a very short list of materials of construction.
And very exacting test requirements.
As I recall our impacts had to be centered on the weld/HAZ interface.
I have done it cooling in both LH2 and LHe.
LH2 is not difficult to handle, but people get weird.
And with any liquid gas, don't leave the container sitting.
LO2 will condense on the surface and that is not good.