Stress analysis in of itself is performed the same way, as far as I know. The difference between "regular" pipe stress analysis and "cryogenic" pipe stress analysis is analogous to "regular" pipe stress analysis and "high temperature" pipe stress analysis. That is, use the right materials at the right temperatures at the right stress levels, and ensure your materials undergo the proper inspection/testing to ensure it is fit for the service specified. Also, make sure that the code you use for your stress analysis covers the proposed material.

I recommend speaking to the pipe supplier(s) for additional guidance.