In the UK Generic Design Assessment (GDA) process, there are very few firm requirements. Through the ALARP process, you determine the optimal approach through consideration of safety significance, relevant good practice, and the claims/argument/evidence (CAE) approach.
If you're using ASME standards and your diesel generator system is Safety Class 1, your relevant good practice would be the US NRC Regulatory Guidance. US NRC RG 1.26 would require that you follow ASME Section III (probably Class 3).
I only work in passive plant designs, so I don't have access to any US licensing documentation for current operating US plants to see what they do in practice. You could check FSARs (where available) for US plants to see what they do in practice. The Korean APR1400 is an active plant design currently undergoing Design Certification and they are currently specifying ASME Section III (their DCD is available on the US NRC web page).
The UK GDA documents for the AREVA design would also be a reference point - check their PCSR to see if they were able to justify a non-safety-related design code for their diesels.